又长又慢的缺省源

#include<cstdio>
#include<utility>
#include<cstdlib>
#include<type_traits>
#include<array>
/**
 * 写得死烂，又长又慢。
 * Author:qL
 * todo：
 * Better modInt
 * frac
 * More Poly
 * fix bug of radix_sort
 * new IO
 * turn std::enable_if into static_assert 
*/
namespace QL{
	/**
	 * 图方便用的
	*/
	namespace{
		using ll=long long;
		using ull=unsigned long long;
		using uint=unsigned int;
		using db=double;
		using ld=long double;
#if _GLIBCXX_USE_INT128
		using lll=__int128;
		using ulll=unsigned __int128;
#else
		using lll=long long;
		using ulll=unsigned long long;
#endif
#if _GLIBCXX_NUMERIC&&(__cplusplus>=201703L)
		template<typename _Tp>
		constexpr _Tp Inf=std::numeric_limits<_Tp>::max()/2;
#else
		constexpr int Inf=0x3f3f3f3f;
		constexpr long long llInf=0x3f3f3f3f3f3f3f3f;
		constexpr double dbInf=1e17;
		constexpr long double ldInf=1e22;
#endif
#ifndef _GLIBCXX_CMATH
	#define sqrt __builtin_sqrt
	#define sqrtf __builtin_sqrtf
	#define sqrtl __builtin_sqrtl
	#define ceil __builtin_ceil
	#define ceilf __builtin_ceilf
	#define ceill __builtin_ceill
	#define floor __builtin_floor
	#define floorf __builtin_floorf
	#define floorl __builtin_floorl
	#define log2 __builtin_log2
	#define log __builtin_log
	#define cos __builtin_cos
	#define sin __builtin_sin
	#define tan __builtin_tan
	#define acos __builtin_acos
#endif
#ifndef _GLIBCXX_CSTRING
	#define memset __builtin_memset
	#define memcpy __builtin_memcpy
	#define strlen __builtin_strlen
	#define strcmp __builtin_strcmp
#endif
#ifndef _GLIBCXX_CSTDIO
	#define fwrite __builtin_fwrite
	#define putchar __builtin_putchar
	#define fputc __builtin_fputc
	#define fputs __builtin_fputs
#endif
#ifndef likely
	#define likely(x) __builtin_expect(!!(x),1)
#endif
#ifndef unlikely
	#define unlikely(x) __builtin_expect(!!(x),0)
#endif
	}
	/**
	 * 不想多加头文件了……
	*/
	namespace Error{
		constexpr void make_re(int _seed_=114514){
			std::exit(_seed_);
		}
#ifndef _GLIBCXX_CASSERT
		constexpr bool assert(bool x,const char *reason="Assert: RE"){
			if(unlikely(!x)){
				fputs(reason,stderr);
				fputs(reason,stdout);
				make_re();
			}
			return false;
		}
		constexpr bool assert(bool x,char *reason){
			return assert(x,const_cast<const char *>(reason));
		}
#endif
	}
}
namespace QL{
	/**
	 * 这坨代码最让人难以理解的地方：没逝乱靠元编程库
	*/
	namespace Traits_Tools{
		template<typename _Tp>
		class has_member_swap{
		private:
			template<typename T>
			static auto Check(void)->decltype(std::declval<T>().swap(),std::true_type());
			template<typename T>
			static std::false_type Check(...);
		public:
			enum{value=std::is_same<decltype(Check<_Tp>(nullptr)),std::true_type>::value};
		};
		#define Operator_Check_Helper(name,opt) \
				template<typename _Tp1,typename _Tp2> \
				class has_operator_##name{ \
				private: \
					template<typename T1,typename T2> \
					static auto Check(void)->decltype(std::declval<T1,T2>().operator opt (),std::true_type()); \
					template<typename T1,typename T2> \
					static std::false_type Check(...); \
				public: \
					enum{value=std::is_same<decltype(Check<_Tp1,_Tp2>(nullptr)),std::true_type>::value}; \
				};
		Operator_Check_Helper(plus,+)
		Operator_Check_Helper(subtract,-)
		Operator_Check_Helper(multiply,*)
		Operator_Check_Helper(divide,/)
		Operator_Check_Helper(mod,%)
		Operator_Check_Helper(and,&)
		Operator_Check_Helper(or,|)
		Operator_Check_Helper(xor,^)
		#undef Operator_Check_Helper
		template<typename _Tp,typename std::enable_if<std::is_integral<_Tp>::value>::type* =nullptr>
		struct to_upper_type;
		#define To_Upper_Helper(_type_,_upper_) \
		template<> \
		struct to_upper_type< _type_ >{ \
			using type=_upper_; \
		}; \
		template<> \
		struct to_upper_type< u##_type_ >{ \
			using type=u##_upper_; \
		};
		To_Upper_Helper(int,ll)
		To_Upper_Helper(ll,lll)
		#undef To_Upper_Helper
	}
}
namespace QL{
	namespace rel_ops{
		namespace Calc_Self{
			#define Calc_Self_Helper(opt) \
			template<typename _Tp1,typename _Tp2> \
			constexpr _Tp1 &operator opt##=(_Tp1 &lhs,const _Tp2 &rhs){ \
				return lhs=(lhs opt rhs); \
			}
			Calc_Self_Helper(+)
			Calc_Self_Helper(-)
			Calc_Self_Helper(*)
			Calc_Self_Helper(/)
			Calc_Self_Helper(%)
			Calc_Self_Helper(&)
			Calc_Self_Helper(|)
			Calc_Self_Helper(^)
			#undef Calc_Self_Helper
		}
		namespace Compare{
			template<typename _Tp1,typename _Tp2>
			constexpr bool operator!=(const _Tp1 &lhs,const _Tp2 &rhs){
				return !(lhs==rhs);
			}
			template<typename _Tp1,typename _Tp2>
			constexpr bool operator<=(const _Tp1 &lhs,const _Tp2 &rhs){
				return (lhs==rhs)||(lhs<rhs);
			}
			template<typename _Tp1,typename _Tp2>
			constexpr bool operator>(const _Tp1 &lhs,const _Tp2 &rhs){
				return !((lhs==rhs)||(lhs<rhs));
			}
			template<typename _Tp1,typename _Tp2>
			constexpr bool operator>=(const _Tp1 &lhs,const _Tp2 &rhs){
				return !(lhs<rhs);
			}
		}
	}
}
/**
 * todo:
 * rebuild
 */
namespace QL{
	namespace Base_Tools{
		template<typename _Tp>
		static constexpr std::size_t integer_length=sizeof(_Tp)*10/sizeof(int);
		bool is_space(char ch){
			return ch==' ';
		}
		bool is_eoln(char ch){
#if (linux||__linux__||__linux)
			return ch=='\n'||ch=='\r';
#else
			return ch=='\n';
#endif
		}
		bool is_blank(char ch){
			return is_space(ch)||is_eoln(ch);
		}
		bool is_digit(char ch){
			switch(ch){
				case '0' ... '9': return true;
				default: return false;
			}
		}
		bool is_eof(char ch){
			return ch==EOF;
		}
	}
	namespace IO{
		using Base_Tools::integer_length;
		using Base_Tools::is_digit;
		using Base_Tools::is_space;
		using Base_Tools::is_eoln;
		using Base_Tools::is_blank;
		using Base_Tools::is_eof;
		/**
		 * fread+fwrite,-DLOACL for debug
		 * support:integer,floating,string,...
		 * todo:other
 		*/
		class IOstream{
		protected:
			using LIST=std::initializer_list<int>;
#ifndef LOCAL
			std::FILE *IN;
			std::FILE *OUT;
			static constexpr int SIZE=1<<15;
			char buf[SIZE]{},*p1{buf},*p2{buf},obuf[SIZE]{},*p3{obuf};
		public:
			char pull(){return p1==p2&&(p2=(p1=buf)+fread(buf,1,SIZE,IN),p1==p2)?(Ch=EOF):*p1++;}
			void push(char ch){((p3-obuf)==SIZE&&(flush(false),0)),*p3++=ch;}
			template<std::size_t L>
			std::FILE *set_in(const char (&name)[L]){
				static char in[L+5]={};
				std::sprintf(in,"%s.in",name);
				return std::fopen(in,"r");
			}
			template<std::size_t L>
			std::FILE *set_out(const char (&name)[L]){
				static char out[L+5];
				std::sprintf(out,"%s.out",name);
				return std::fopen(out,"w");
			}
#else
		protected:
		public:
			char pull(){return std::getchar();}
			void push(char ch){putchar(ch);}
			void err(char ch){fputc(ch,stderr);}
			template<std::size_t L>
			void set_in(const char(&name)[L]){
				static char in[L+5]={};
				std::sprintf(in,"%s.in",name);
				std::freopen(in,"r",stdin);
			}
			template<std::size_t L>
			void set_out(const char(&name)[L]){
				static char out[L+5];
				std::sprintf(out,"%s.out",name);
				std::freopen(out,"w",stdout);
			}
#endif
		public:
#ifndef LOCAL
			IOstream():IN{stdin},OUT{stdout},buf{},p1{buf},p2{buf},obuf{},p3{obuf},Ch{'\n'},outchar{&IO::IOstream::push}{}
			template<std::size_t L>
			IOstream(const char(&name)[L]):IN{set_in(name)},OUT{set_out(name)},buf{},p1{buf},p2{buf},obuf{},p3{obuf},Ch{'\n'},outchar{&IO::IOstream::push}{}
			template<std::size_t L>
			IOstream(const char(&name)[L],bool in,bool out):IN{in?set_in(name):stdin},OUT{out?set_out(name):stdout},buf{},p1{buf},p2{buf},obuf{},p3{obuf},Ch{'\n'},outchar{&IO::IOstream::push}{}
			template<std::size_t L>
			IOstream(char(&name)[L]):IN{set_in(name)},OUT{set_out(name)},buf{},p1{buf},p2{buf},obuf{},p3{obuf},Ch{'\n'},outchar{&IO::IOstream::push}{}
			template<std::size_t L>
			IOstream(char(&name)[L],bool in,bool out):IN{in?set_in(name):stdin},OUT{out?set_out(name):stdout},buf{},p1{buf},p2{buf},obuf{},p3{obuf},Ch{'\n'},outchar{&IO::IOstream::push}{}
			~IOstream(){flush();}
			void flush(bool _flush_=false){
				if(likely(p3!=obuf))
					fwrite(obuf,1,p3-obuf,OUT),p3=obuf;
				if(_flush_) std::fflush(stdout);
			}
#else
			IOstream(){}
			template<std::size_t L>
			IOstream(const char(&name)[L]):Ch{'\n'}{reset_stdin(name),reset_stdout(name);}
			template<std::size_t L>
			IOstream(const char(&name)[L],bool in,bool out):Ch{'\n'}{in&&(reset_stdin(name),0),out&&(reset_stdout(name),0);}
			template<std::size_t L>
			IOstream(char(&name)[L]):Ch{'\n'}{reset_stdin(name),reset_stdout(name);}
			template<std::size_t L>
			IOstream(char(&name)[L],bool in,bool out):Ch{'\n'}{in&&(reset_stdin(name),0),out&&(reset_stdout(name),0);}
			void flush(bool _flush_=true){
				if(_flush_) std::fflush(stdout);
			}
#endif
			template<typename T>
			T read(){
				T x;
				read(x);
				return x;
			}
protected:
			char Ch='\n';
public:
			bool eof(void)const{
				return Ch==EOF;
			}
			template<typename T>
			void read(T &&x,typename std::enable_if<std::is_integral<T>::value,void>::type* =nullptr,typename std::enable_if<std::is_signed<T>::value,void>::type* =nullptr){
				x=0;bool flag=0;
				for(;!is_digit(Ch)&&!is_eof(Ch);Ch=pull()) if(Ch=='-') flag=1;
				if(is_eof(Ch)) return;
				if(flag) for(;is_digit(Ch);Ch=pull()) x=x*10-(Ch&15);
				else for(;is_digit(Ch);Ch=pull()) x=x*10+(Ch&15);
			}
			template<typename T>
			void read(T &&x,typename std::enable_if<std::is_integral<T>::value,void>::type* =nullptr,typename std::enable_if<std::is_unsigned<T>::value,void>::type* =nullptr){
				x=0;
				for(;!is_digit(Ch)&&!is_eof(Ch);Ch=pull());
				if(is_eof(Ch)) return;
				for(;is_digit(Ch);Ch=pull()) x=x*10+(Ch&15);
			}
			void read(char *str){
				for(;is_blank(Ch);Ch=pull());
				if(is_eof(Ch)) return (void)(*str='\0');
				for(;!is_blank(Ch)&&!is_eof(Ch);Ch=pull()) *str++=Ch;
				*str='\0';
			}
			void read(char &c){
				c=Ch;
				for(;is_blank(c)&&!is_eof(c);c=pull());
				if(is_eof(c)) return;
				Ch=pull();
			}
			void read(bool &x){
				for(;Ch!='0'&&Ch!='1'&&!is_eof(Ch);Ch=pull());
				if(is_eof(Ch)) return void(x=false);
				x=Ch=='1';
				Ch=pull();
			}
			template<typename T>
			void read(T &&x,typename std::enable_if<std::is_floating_point<T>::value,void*>::type* =nullptr){
				static char str[114];
				read(str);
				x=std::atof(str);
			}
			template<typename T>
			void read(T &x){read(std::move(x));}
		protected:
			void(IOstream::*outchar)(char)=&IO::IOstream::push;
			template<typename T>
			void out(T x,typename std::enable_if<std::is_integral<T>::value,void>::type* =nullptr,typename std::enable_if<std::is_signed<T>::value,void>::type* =nullptr){
				static char sta[integer_length<T>];
				int top=0;
				if(x<0){
					(this->*outchar)('-');
					do sta[top++]=((-x)%10)|48,x/=10;
					while(x);
				}
				else{
					do sta[top++]=(x%10)|48,x/=10;
					while(x);
				}
				while(top) (this->*outchar)(sta[--top]);
			}
			template<typename T>
			void out(T x,typename std::enable_if<std::is_integral<T>::value,void>::type* =nullptr,typename std::enable_if<std::is_unsigned<T>::value,void>::type* =nullptr){
				static char sta[integer_length<T>];
				int top=0;
				do sta[top++]=(x%10)|48,x/=10;
				while(x);
				while(top) (this->*outchar)(sta[--top]);
			}
			void out(bool x){(this->*outchar)(x?'1':'0');}
			void out(char x){(this->*outchar)(x);}
			void out(char *str){
				out(reinterpret_cast<const char *>(str));
			}
			void out(const char *str){
				while(*str!='\0') (this->*outchar)(*str++);
			}
			/**
			 * ssprintf is awful...
			 */
			void out(float x){
				static char str[114];
				std::sprintf(str,"%f",x);
				out(str);
			}
			void out(double x){
				static char str[114];
				std::sprintf(str,"%f",x);
				out(str);
			}
			void out(long double x){
				static char str[114];
				std::sprintf(str,"%Lf",x);
				out(str);
			}
			void out(std::pair<int,float> x){
				static char str[114],opt[10];
				std::sprintf(opt,"%%.%df",x.first);
				std::sprintf(str,opt,x.second);
				out(str);
			}
			void out(std::pair<int,double> x){
				static char str[114],opt[10];
				std::sprintf(opt,"%%.%df",x.first);
				std::sprintf(str,opt,x.second);
				out(str);
			}
			void out(std::pair<int,long double> x){
				static char str[114],opt[10];
				std::sprintf(opt,"%%.%dLf",x.first);
				std::sprintf(str,opt,x.second);
				out(str);
			}
			void set_std_out(){outchar=&IO::IOstream::push;}
#ifdef LOCAL
			void set_err_out(){outchar=&IO::IOstream::err;}
#endif
		public:
			template<typename...Args>
			void read(Args &&...args){(void)LIST{(read(args),0)...};}
			template<typename...Args>
			void write(Args...args){set_std_out(),(void)LIST{(out(args),0)...};}
			template<typename...Args>
			void writeln(Args...args){write(args...),push('\n');}
#ifdef LOCAL
			template<typename...Args>
			void error(Args...args){set_err_out(),(void)LIST{(out(args),0)...};}
			template<typename...Args>
			void errorln(Args...args){error(args...),err('\n');}
#endif
		};
		IOstream lq;
	}
}
namespace QL{
	/**
	 * gcd is 1 for floating
	*/
	namespace Math_Tools{
		namespace Math_Tools_base{
			template<typename _Tp,typename _Used>
			constexpr _Tp qpow(ull x,_Used p,_Tp mod){
				_Tp ret=1;
				for(;p;p>>=1,x=x*x%mod) if(p&1) ret=ret*x%mod;
				return ret;
			}
		}
		template<typename _Tp,typename _Used>
		constexpr _Tp qpow(_Tp x,_Used p,_Tp mod){
			if(unlikely(x<0)) x=mod+(x%mod);
			return Math_Tools_base::qpow(x,p,mod);
		}
		template<typename _Tp,typename _Used>
		constexpr _Tp qpow(_Tp x,_Used p){
			_Tp ret=1;
			for(;p;p>>=1,x=x*x) if(p&1) ret=ret*x;
			return ret;
		}
		template<typename _Tp>
		constexpr _Tp inv(_Tp x,_Tp mod){
			return Math_Tools_base::qpow(x,mod-2,mod);
		}
		template<typename _Tp>
		constexpr auto gcd(_Tp a,_Tp b,typename std::enable_if<std::is_integral<_Tp>::value>::type* =nullptr){
			return b?gcd(b,a%b):a;
		}
		template<typename _Tp>
		constexpr auto gcd(_Tp a,_Tp b,typename std::enable_if<std::is_floating_point<_Tp>::value>::type* =nullptr){
			return 1;
		}
		template<typename _Tp>
		constexpr auto lcm(_Tp a,_Tp b){
			return a/gcd(a,b)*b;
		}
	}
}
namespace QL{
	/**
	 * 一个不成型的东西
	 * 日后补全
	 */
	namespace FracNumber{
		using Math_Tools::lcm;
		using Math_Tools::gcd;
		template<typename _Tp>
		class frac{
		protected:
			_Tp x,y;
			constexpr void chk_self(){
				_Tp _gcd_=gcd(x,y);
				if(_gcd_!=1) x/=_gcd_,y/=_gcd_;
			}
		public:
			constexpr frac():x{},y{}{}
			template<typename T>
			constexpr frac(T num,typename std::enable_if<std::is_integral<T>::value,void>::type* =nullptr):x(num),y(1){}
			template<typename T>
			constexpr frac(T _x,T _y,typename std::enable_if<std::is_integral<T>::value,void>::type* =nullptr):x(_x),y(_y){chk_self();}
			template<typename T>
			constexpr explicit operator T()const{
				return T(x)/y;
			}
			template<typename T>
			constexpr bool operator<(const frac<T> &it)const{
				auto _lcm_=lcm(y,it.y);
				return x*(_lcm_/y)<it.x*(_lcm_/it.y);
			}
		};
	}
}
namespace QL{
	/**
	 * 本实现的亮点是支持不定模数（不用遍历地进行初始化）
	 * 需要实现一个类，重载const类型的()运算符返回模数
	 * 实现可参考QL::ModNumber::Moder
	 * 模数有问题可以重载inv
	 * 其他的不知道了，似乎不是很快，要卡常的可以套约减器
	 * （用这玩意儿也就图个方便）
	 * upd：塞进去了个barrett约减，更慢了（乐
	 * 跑不过编译器优化，它是蒙哥马利吗……
	 * todo:
	 * rebuild because of some bugs here
	 */
	namespace ModNumber{
		template<typename _Tp>
		class Barrett{
			_Tp mod;
			ulll used;
		public:
			Barrett(){}
			Barrett(_Tp _mod):mod{_mod},used{(ulll(1)<<63)/mod}{}
			constexpr void ReInit(_Tp _mod){mod=_mod,used=(ulll(1)<<63)/mod;}
			constexpr _Tp calc(ll x)const{return (x=x-mod*((x*used)>>63))<mod?x:x-mod;}
		};
		template<typename _Tp>
		class Base_mod{
			static_assert(std::is_integral<_Tp>::value,"In Moder(class): The type must be an integer.");
		public:
			constexpr _Tp operator()()const{return 1e9+7;}
			template<typename T>
			constexpr _Tp inv(T a){
				static_assert(std::is_integral<T>::value,"In Base_mod(class): The type to calc inv must be an integer.");
				_Tp mod=this->operator()(),x=mod-2,ret=1;
				for(;x;x>>=1,a=ll(a)*a%mod) if(x&1) ret=ret*ll(a)%mod;
				return ret;
			}
		};
		template<typename _Tp,template<typename> class _Mod>
		class Prim_Calcer{
			static_assert(std::is_integral<_Tp>::value,"In Moder(class): The type must be an integer.");
		protected:
			_Mod<_Tp> mod;
		public:
			template<typename T>
			_Tp calc(T x){return x%mod();}
		};
		template<typename _Tp,template<typename> class _Mod=Base_mod,template<typename,template<typename> class> class _Calcer=Prim_Calcer>
		class Moder{
			static_assert(std::is_integral<_Tp>::value,"In Moder(class): The type must be an integer.");
		protected:
			static _Mod<_Tp> mod;
			static _Calcer<_Tp,_Mod> calcer;
		public:
			const _Tp operator()(void)const{return mod();}
			template<typename T>
			constexpr void chk_val(T &val)const{val<0?(val+=mod()):(val<mod()?0:val-=mod());}
			template<typename T>
			constexpr T calc(const T &x)const{return calcer.calc(x);}
			template<typename T1,typename T2>
			constexpr _Tp plus(const T1 &x,const T2 &y)const{return calcer.calc(x+y);}
			template<typename T1,typename T2>
			constexpr _Tp mul(const T1 &x,const T2 &y)const{return calcer.calc(ll(x)*y);}
			template<typename T>
			constexpr _Tp inv(const T &x)const{
				return mod.inv(x);
			}
		};
		template<typename _Tp,template<typename> class _Mod,template<typename,template<typename> class> class _Calcer>
		_Mod<_Tp> Moder<_Tp,_Mod,_Calcer>::mod;
		template<typename _Tp,template<typename> class _Mod,template<typename,template<typename> class> class _Calcer>
		_Calcer<_Tp,_Mod> Moder<_Tp,_Mod,_Calcer>::calcer;
		template<typename _Tp=int,template<typename> class _Mod=Base_mod,template<typename,template<typename> class> class _Calcer=Prim_Calcer,template<typename,template<typename> class,template<typename,template<typename> class> class> class _Moder=Moder>
		class modInt{
			static_assert(std::is_signed<_Tp>::value,"In modInt(class): The type must be signed.");
		protected:
			static _Moder<_Tp,_Mod,_Calcer> moder;
			_Tp v;
		public:
			constexpr modInt():v{}{}
			template<typename T>
			constexpr modInt(const T &_v):v(_v%moder()){
				static_assert(std::is_integral<T>::value,"In modInt(class): The value must be an integer.");
			}
			constexpr modInt(const modInt &_it):v{_it.v}{}
			template<typename T>
			constexpr explicit operator T()const{return v;}
			constexpr modInt operator-()const{
				return modInt(moder()-v);
			}
			constexpr modInt operator+(const modInt &y)const{
				return moder.plus(v,y.v);
			}
			constexpr modInt operator-(const modInt &y)const{
				return *this+(-y);
			}
			constexpr modInt operator*(const modInt &y)const{
				return moder.mul(v,y.v);
			}
			constexpr modInt operator/(const modInt &y)const{
				return moder.mul(v,moder.inv(y.v));
			}
			#define MODINT_T_HELPER(opt) \
			template<typename T> \
			constexpr friend modInt operator opt (const modInt &x,const T &y){ \
				return x opt modInt(y); \
			}
			MODINT_T_HELPER(+)
			MODINT_T_HELPER(-)
			MODINT_T_HELPER(*)
			MODINT_T_HELPER(/)
			#undef MODINT_T_HELPER
			#define MODINT_REV_HELPER(opt) \
			template<typename T> \
			constexpr friend modInt operator opt (const T &x,const modInt &y){ \
				return modInt(x) opt y; \
			}
			MODINT_REV_HELPER(+)
			MODINT_REV_HELPER(-)
			MODINT_REV_HELPER(*)
			MODINT_REV_HELPER(/)
			#undef MODINT_REV_HELPER
			template<typename T>
			constexpr friend bool operator<(const T &x,const modInt &y){return x<y.v;}
			template<typename T>
			constexpr bool operator<(const T &y)const{return v<y;}
			template<typename T>
			constexpr friend bool operator==(const T &x,const modInt &y){return x==y.v;}
			template<typename T>
			constexpr bool operator==(const T &y)const{return v==y;}
			constexpr modInt &operator++(){
				moder.chk_val(++v);
				return *this;
			}
			constexpr modInt operator++(int){
				modInt ret=*this;
				moder.chk_val(++v);
				return ret;
			}
			constexpr modInt &operator--(){
				moder.chk_val(--v);
				return *this;
			}
			constexpr modInt operator--(int){
				modInt ret=*this;
				moder.chk_val(--v);
				return ret;
			}
			template<typename T>
			constexpr modInt qpow(T x)const{
				modInt ret(1),a{*this};
				for(;x;x>>=1,a=a*a) if(x&1) ret=ret*a;
				return ret;
			}
		};
		template<typename _Tp,template<typename> class _Mod,template<typename,template<typename> class> class _Calcer,template<typename,template<typename> class,template<typename,template<typename> class> class> class _Moder>
		_Moder<_Tp,_Mod,_Calcer> modInt<_Tp,_Mod,_Calcer,_Moder>::moder;
	}
}
namespace QL{
	namespace Algorithm{
		using Base_Tools::swap;
		template<typename _Tp>
		void radix_sort(_Tp *x,int n,typename std::enable_if<std::is_integral<_Tp>::value,void>::type* =nullptr){
			static const int mask=(1<<8)-1;
			static int *cnt=new int[mask+1],*y=new int[n+5];
			for(int k=0;k<32;k+=8){
				for(int i=0;i<=mask;++i) cnt[i]=0;
				for(int i=1;i<=n;++i) ++cnt[(x[i]>>k)&mask];
				for(int sum=0,i=0;i<=mask;++i)
					sum+=cnt[i],cnt[i]=sum-cnt[i];
				for(int i=1;i<=n;++i) y[++cnt[(x[i]>>k)&mask]]=x[i];
				swap(x,y);
			}
		}
		template<typename _Tp,typename _Turn>
		void radix_sort(_Tp *x,int n,_Turn turn){
			static const int mask=(1<<8)-1;
			static int *cnt=new int[mask+1],*y=new int[n+5];
			for(int k=0;k<32;k+=8){
				for(int i=0;i<=mask;++i) cnt[i]=0;
				for(int i=1;i<=n;++i) ++cnt[(turn(x[i])>>k)&mask];
				for(int sum=0,i=0;i<=mask;++i)
					sum+=cnt[i],cnt[i]=sum-cnt[i];
				for(int i=1;i<=n;++i) y[++cnt[(turn(x[i])>>k)&mask]]=x[i];
				swap(x,y);
			}
		}
		template<typename _Tp>
		void radix_sort(_Tp *x,int n,int (*turn)(_Tp)){
			static const int mask=(1<<8)-1;
			static int *cnt=new int[mask+1],*y=new int[n+5];
			for(int k=0;k<32;k+=8){
				for(int i=0;i<=mask;++i) cnt[i]=0;
				for(int i=1;i<=n;++i) ++cnt[(turn(x[i])>>k)&mask];
				for(int sum=0,i=0;i<=mask;++i)
					sum+=cnt[i],cnt[i]=sum-cnt[i];
				for(int i=1;i<=n;++i) y[++cnt[(turn(x[i])>>k)&mask]]=x[i];
				swap(x,y);
			}
		}
		template<typename _Iterator>
		constexpr void reverse(_Iterator _st,_Iterator _ed){
			--_ed;
			for(;_st!=_ed;++_st,--_ed) swap(_st,_ed);
		}
	}
}
#if __cplusplus<201703L
namespace QL{
	namespace Array{
		template<typename _Tp,unsigned N>
		class array{
		private:
			_Tp arr[N];
		public:
			constexpr unsigned size()const{return N;}
			constexpr _Tp &operator[](unsigned _n){
				return arr[_n];
			}
			constexpr _Tp operator[](unsigned _n)const{
				return arr[_n];
			}
		};
	}
}
#endif
namespace QL{
	/**
	 * 字符串的工具
	 */
	namespace String_Tools{
		namespace SA{
			template<int M=128,int N>
			void calc_sa(char (&str)[N],int sa[],int rk[],int n){
				int m=M-1;
				static int cnt[N<M?M:N],id[N],oldrk[N<<1],key[N];
				for(int i=1;i<=n;++i) ++cnt[rk[i]=str[i]];
				for(int i=1;i<=m;++i) cnt[i]+=cnt[i-1];
				for(int i=n;i;--i) sa[cnt[rk[i]]--]=i;
				for(int k=1,p;;k<<=1,m=p){
					p=0;
					for(int i=n;i>n-k;--i) id[++p]=i;
					for(int i=1;i<=n;++i) if(sa[i]>k) id[++p]=sa[i]-k;
					memset(cnt,0,sizeof(int)*(m+1));
					for(int i=1;i<=n;++i) ++cnt[key[i]=rk[id[i]]];
					for(int i=1;i<=m;++i) cnt[i]+=cnt[i-1];
					for(int i=n;i;--i) sa[cnt[key[i]]--]=id[i];
					memcpy(oldrk,rk,sizeof(int)*(n+1));
					p=0;
					for(int i=1;i<=n;++i){
						static auto cmp=[&k](int x,int y){
							return oldrk[x]==oldrk[y]&&oldrk[x+k]==oldrk[y+k];
						};
						rk[sa[i]]=cmp(sa[i],sa[i-1])?p:++p;
					}
					if(p==n) return;
				}
			}
			template<int N>
			constexpr void calc_height(char (&str)[N],int sa[],int rk[],int height[],int n){
				for(int i=1,k=0;i<=n;++i){
					if(!rk[i]) continue;
					k&&--k;
					for(;str[i+k]==str[sa[rk[i]-1]+k];++k);
					height[rk[i]]=k;
				}
			}
		}
	}
}
namespace QL{
	/**
	 * 多项式，占坑
	 * 以后会尽量补全的
	 * todo:
	 * length
	 * Memory Pool
	 */
	namespace Poly_Tools{
		namespace Poly_Base{
			constexpr uint max_g=22,max_len=2<<20;
			constexpr uint pw[]{0,1,2,4,8,16,32,64,128,256,512,1024};
			uint rev[max_len];
			constexpr void ReInit(uint n){
				for(uint i(0);i<n;++i) rev[i]=(rev[i>>1]>>1)|((i&1)?(n>>1):0);
			}
			constexpr uint to_up(uint x){
				#define cs(x) case pw[x] ... pw[x+1]-1: return pw[x+1];
				switch(x){
					cs(0)cs(1)cs(2)cs(3)cs(4)cs(5)cs(6)cs(7)cs(8)cs(9)cs(10)
					default: return 1u<<(32-__builtin_clz(x));
				}
				#undef cs
			}
		}
		namespace ComplexNumber{
			template<typename _Tp>
			struct complex{
				static_assert(std::is_floating_point<_Tp>::value,"In complex(class), the type must be floating point.");
				_Tp real,imag;
				constexpr complex():real{},imag{}{}
				template<typename T>
				constexpr complex(const T &_real):real(_real),imag{}{}
				template<typename T1,typename T2>
				constexpr complex(const T1 &_real,const T2 &_imag):real(_real),imag(_imag){}
				template<typename T>
				constexpr complex(const complex<T> &it):real(it.real),imag(it.imag){}
				constexpr complex operator+(const complex &it)const{
					return complex(real+it.real,imag+it.imag);
				}
				constexpr complex operator-(const complex &it)const{
					return complex(real-it.real,imag-it.imag);
				}
				constexpr complex operator*(const complex &it)const{
					return complex(real*it.real-imag*it.imag,imag*it.real+real*it.imag);
				}
			};
		}
		namespace Primitive_Root{
#if __cplusplus<201703L
			template<typename _Tp,unsigned N>
			using array=QL::Array::array<_Tp,N>;
#else
			template<typename _Tp,unsigned N>
			using array=std::array<_Tp,N>;
#endif
			template<typename _U_Tp>
			static constexpr auto init_for_gn(_U_Tp p,_U_Tp g){
				static_assert(std::is_integral<_U_Tp>::value,"In const_Prim_Root(class): The type must be an integral.");
				array<_U_Tp,Poly_Base::max_g> ret{};
				for(uint i(0);i<Poly_Base::max_g;++i) ret[i]=Math_Tools::qpow(g,(p-1)>>i,p);
				return ret;
			}
			template<typename _U_Tp>
			static constexpr auto init_for_inv(_U_Tp p,_U_Tp g){
				static_assert(std::is_integral<_U_Tp>::value,"In const_Prim_Root(class): The type must be an integral.");
				array<_U_Tp,Poly_Base::max_g> ret{};
				_U_Tp v=Math_Tools::inv(g,p);
				for(uint i(0);i<Poly_Base::max_g;++i) ret[i]=Math_Tools::qpow(v,(p-1)>>i,p);
				return ret;
			}
			struct Prim_Root{};
			/**
			 * todo:
			 * find the prim root
			 * support more types
			*/
			struct runtime_Prim_Root:Prim_Root{
				uint p,g;
				array<uint,Poly_Base::max_g> gn,inv;
				runtime_Prim_Root():p{},g{},gn{},inv{}{}
				runtime_Prim_Root(uint _p,uint _g):p{_p},g{_g},gn{init_for_gn(p,g)},inv{init_for_inv(g,p)}{}
			};
			template<typename _U_Tp,_U_Tp _p,_U_Tp _g>
			struct const_Prim_Root:Prim_Root{
				static_assert(std::is_integral<_U_Tp>::value,"In const_Prim_Root(class): The type must be an integral.");
				static constexpr _U_Tp p{_p},g{_g};
				static constexpr array<_U_Tp,Poly_Base::max_g> gn{init_for_gn(_p,_g)},inv{init_for_inv(_p,_g)};
			};
			template<typename _U_Tp,_U_Tp _p,_U_Tp _g>
			constexpr _U_Tp const_Prim_Root<_U_Tp,_p,_g>::p;
			template<typename _U_Tp,_U_Tp _p,_U_Tp _g>
			constexpr _U_Tp const_Prim_Root<_U_Tp,_p,_g>::g;
			template<typename _U_Tp,_U_Tp _p,_U_Tp _g>
			constexpr array<_U_Tp,Poly_Base::max_g> const_Prim_Root<_U_Tp,_p,_g>::gn;
			template<typename _U_Tp,_U_Tp _p,_U_Tp _g>
			constexpr array<_U_Tp,Poly_Base::max_g> const_Prim_Root<_U_Tp,_p,_g>::inv;
			using G_998244353i=const_Prim_Root<uint,998244353,3>;
			using G_1004535809i=const_Prim_Root<uint,1004535809,3>;
			using G_46976204i=const_Prim_Root<uint,469762049,3>;
		}
		/**
		 * 暴力乘法（划掉）
		 * upd:FFT
		 */
		using Base_Tools::swap;
		using namespace rel_ops::Calc_Self;
		namespace Poly_Base{
			template<typename _Tp>
			class Poly{
			protected:
				_Tp *p;
				uint n;
			public:
				constexpr uint length(void)const{return n;}
				constexpr Poly():p{},n{}{}
				constexpr Poly(const uint &_n):p{new _Tp[_n]{}},n{_n}{}
				constexpr Poly(const std::initializer_list<_Tp> &L){
					delete[] p;
					p=new _Tp[L.size()]{},n=0;
					for(auto it:L) p[n++]=it;
				}
				constexpr Poly(const Poly &it):n{it.n}{
					p=new _Tp[it.n]{},n=it.n;
					memcpy(p,it.p,sizeof(_Tp)*it.n);
				}
				constexpr void resize(const uint &_n){
					delete[] p;
					p=new _Tp[_n]{},n=_n;
				}
				constexpr Poly &operator=(const Poly &it){
					if(this==&it) return *this;
					delete[] p;
					p=new _Tp[it.n]{},n=it.n;
					memcpy(p,it.p,sizeof(_Tp)*it.n);
					return *this;
				}
				constexpr _Tp &operator[](const uint &x){
					if(x>=n) Error::make_re();
					return p[x];
				}
				constexpr const _Tp &operator[](const uint &x)const{
					if(x>=n) Error::make_re();
					return p[x];
				}
				~Poly(){
					delete[] p;
				}
			};
		}
		namespace Transforms{
			namespace For_FFT{
				using Complex=ComplexNumber::complex<db>;
				Complex f[Poly_Base::max_len];
				constexpr db PI=acos(-1);
				template<bool type>
				constexpr void FFT_transform(Complex *f,uint n){
					for(uint i(0);i<n;++i) if(i<Poly_Base::rev[i]) swap(f[i],f[Poly_Base::rev[i]]);
					for(uint p(1),l(2);l<=n;p=l,l<<=1){
						Complex step(cos(PI/p),type?sin(PI/p):-sin(PI/p));
						for(uint i(0);i<n;i+=l){
							Complex *g=f+i,*h=g+p,w(1,0),t;
							for(uint k(0);k<p;++k,w=w*step)
								t=h[k]*w,h[k]=g[k]-t,g[k]=g[k]+t;
						}
					}
				}
			}
		}
		template<typename _Tp>
		class FFT:public Poly_Base::Poly<_Tp>{
			using Poly=Poly_Base::Poly<_Tp>;
		public:
			constexpr FFT():Poly(){}
			constexpr FFT(const Poly &poly):Poly(poly){}
			constexpr Poly operator*(const FFT<_Tp> &it){
				using namespace Transforms::For_FFT;
				Poly ret(Poly::n+it.length()-1);
				uint x(Poly_Base::to_up(ret.length()));
				for(uint i(0);i<x;++i) f[i]=Complex(0,0);
				for(uint i(0);i<Poly::n;++i) f[i].real=Poly::p[i];
				for(uint i(0);i<it.length();++i) f[i].imag=it[i];
				Poly_Base::ReInit(x);
				FFT_transform<true>(f,x);
				for(uint i(0);i<x;++i) f[i]*=f[i];
				FFT_transform<false>(f,x);
				for(uint i(0);i<ret.length();++i) ret[i]=f[i].imag/x/2.0+0.5;
				return ret;
			}
		};
		namespace Transforms{
			namespace For_NTT{
				template<bool type,typename _Prim_Root>
				constexpr void NTT_transform(ull *f,uint n,const _Prim_Root &pr){
					static_assert(std::is_base_of<Primitive_Root::Prim_Root,_Prim_Root>::value,"In NTT(transform): Prim_Root is invalid,Please use the class in QL::Primitive_Root.");
					for(uint i(0);i<n;++i) if(i<Poly_Base::rev[i]) swap(f[i],f[Poly_Base::rev[i]]);
					for(uint p(1),l(2),d(1);l<=n;p=l,l<<=1,++d){
						ull step(type?pr.gn[d]:pr.inv[d]);
						for(uint i(0);i<n;i+=l){
							ull *g=f+i,*h=g+p,w(1),t;
							for(uint k(0);k<p;++k,w=w*step%pr.p)
								t=h[k]*w%pr.p,h[k]=(g[k]+pr.p-t)%pr.p,g[k]=(g[k]+t)%pr.p;
						}
					}
				}
				ull f[Poly_Base::max_len],g[Poly_Base::max_len];
			}
		};
		template<typename _Tp,typename _Prim_Root=Primitive_Root::G_998244353i>
		class NTT:public Poly_Base::Poly<_Tp>{
			using Poly=Poly_Base::Poly<_Tp>;
			static _Prim_Root pr;
			static_assert(std::is_integral<_Tp>::value,"In NTT(class): The type is not an integral.");
			static_assert(std::is_base_of<Primitive_Root::Prim_Root,_Prim_Root>::value,"In NTT(class): Prim_Root is invalid,Please use the class in QL::Primitive_Root.");
		public:
			constexpr NTT():Poly(){}
			constexpr NTT(const Poly &poly):Poly(poly){}
			constexpr Poly operator*(const NTT<_Tp,_Prim_Root> &it){
				using namespace Transforms::For_NTT;
				Poly ret(Poly::n+it.length()-1);
				uint x(Poly_Base::to_up(ret.length()));
				for(uint i(0);i<Poly::n;++i) f[i]=Poly::p[i];
				for(uint i(Poly::n);i<x;++i) f[i]=0;
				for(uint i(0);i<it.length();++i) g[i]=it[i];
				for(uint i(it.length());i<x;++i) g[i]=0;
				Poly_Base::ReInit(x);
				NTT_transform<true>(f,x,pr);
				NTT_transform<true>(g,x,pr);
				for(uint i(0);i<x;++i) f[i]=f[i]*g[i]%pr.p;
				NTT_transform<false>(f,x,pr);
				for(uint i(0);i<ret.length();++i) ret[i]=f[i]*Math_Tools::qpow(x,pr.p-2,pr.p)%pr.p;
				return ret;
			}
		};
		template<typename _Tp,typename _Prim_Root>
		_Prim_Root NTT<_Tp,_Prim_Root>::pr;
	}
}
namespace MAIN{
	using namespace QL;
	using IO::lq;
	void _main_(void){
		return;
	}
}
signed main(){
	return MAIN::_main_(),0;
}