数论模板初期...
大小只有10k左右....并不是很全....里面有手打的modint,bitset和hashmap(O(1)清空..)
#include <cmath>
#include <cstdio>
#include <cstring>
#define fon(i,s) for(int i=0;i<s; ++i)
#define fone(i,s) for(int i=0;i<=s;++i)
#define fox(i,f,t) for(int i=f;i<t; ++i)
#define foxe(i,f,t) for(int i=f;i<=t;++i)
#define fdn(i,s) for(int i=s;i; --i)
#define fdne(i,s) for(int i=s;~i; --i)
#define fdx(i,f,t) for(int i=f;i>t; --i)
#define fdxe(i,f,t) for(int i=f;i>=t;--i)
namespace _nt{
#define mod 998244353
#define modll 998244353
struct intm{
int n;
inline intm(){ n=0; }
inline intm(int nx){ n=nx%mod; }
inline intm(long long nx){ n=nx&((2<<31)-1); }
friend inline intm operator+(intm a,intm b){ return intm(a.n+b.n); }
friend inline intm operator-(intm a,intm b){ return intm(a.n-b.n+mod); }
friend inline intm operator*(intm a,intm b){ return intm((long long)a.n*b.n&modll); }
friend inline intm operator^(intm a,int b){
intm u(1);
while(b){
if(b&1) u=u*a;
a=a*a,b>>=1;
}
return u;
}
friend inline intm operator^(intm a,long long b){
intm u(1);
while(b){
if(b&1) u=u*a;
a=a*a,b>>=1;
}
return u;
}
friend inline intm operator^(intm a,unsigned long long b){
intm u(1);
while(b){
if(b&1) u=u*a;
a=a*a,b>>=1;
}
return u;
}
friend inline intm operator^(intm a,unsigned int b){
intm u(1);
while(b){
if(b&1) u=u*a;
a=a*a,b>>=1;
}
return u;
}
friend inline intm operator^(intm a,intm b){
return a^(b.n);
}
friend inline intm operator~(intm a){
return a^(mod-2);
}
friend inline intm operator/(intm a,intm b){
return a*(~b);
}
};
struct bitset_u{
unsigned long long u;
inline bitset_u(){
u=0ll;
}
inline bitset_u(unsigned long long a){u=a;}
inline bool get(int n){
return (u>>n)&1;
}
inline void set(int n,bool p){
u=(u|(1<<n))&p<<n;
}
inline bitset_u operator<<(int n){
return bitset_u(u<<n);
}
inline bitset_u operator>>(int n){
return bitset_u(u>>n);
}
inline bitset_u operator^ (bitset_u n){
return bitset_u(u^n.u);
}
inline bitset_u operator& (bitset_u n){
return bitset_u(u&n.u);
}
inline bitset_u operator| (bitset_u n){
return bitset_u(u|n.u);
}
inline bitset_u operator~ (){
return bitset_u(~u);
}
};
#define maxn 20000010
struct linear_sieve{
bool is[maxn];
int primes[maxn/10],primelen;
inline void operator()(){
is[1]=1;
for(int i=2;i<maxn;++i){
if(!is[i]) primes[primelen++]=i;
for(int j=0;j<primelen;++j){
if(i*primes[j]>=maxn) break;
if(i%primes[j]) is[i*primes[j]]=1; else {
is[i*primes[j]]=1;
break;
}
}
}
}
} ls;
struct linear_sieve_phi{
bool is[maxn];
int primes[maxn/10],primelen,phi[maxn];
inline void operator()(){
is[1]=1;
phi[1]=0;
for(int i=2;i<maxn;++i){
if(!is[i]) primes[primelen++]=i,phi[i]=i-1;
for(int j=0;j<primelen;++j){
if(i*primes[j]>=maxn) break;
if(i%primes[j]) is[i*primes[j]]=1,phi[i*primes[j]]=phi[i]*(primes[j]-1); else {
is[i*primes[j]]=1,phi[i*primes[j]]=phi[i]*primes[j];
break;
}
}
}
}
};
struct linear_sieve_mu{
bool is[maxn];
int primes[maxn/10],primelen,mu[maxn];
inline void operator()(){
is[1]=1;
mu[1]=1;
for(int i=2;i<maxn;++i){
if(!is[i]) primes[primelen++]=i,mu[i]=-1;
for(int j=0;j<primelen;++j){
if(i*primes[j]>=maxn) break;
if(i%primes[j]) is[i*primes[j]]=1,mu[i*primes[j]]=-mu[i]; else {
is[i*primes[j]]=1,mu[i*primes[j]]=0;
break;
}
}
}
}
};
struct linear_sieve_ds{
bool is[maxn];
int primes[maxn/10],primelen,mu[maxn],ds[maxn],dp[maxn];
inline void operator()(){
is[1]=1;
ds[1]=1;
for(int i=2;i<maxn;++i){
if(!is[i]) primes[primelen++]=i,mu[i]=-1;
for(int j=0;j<primelen;++j){
if(i*primes[j]>=maxn) break;
if(i%primes[j]) is[i*primes[j]]=1,ds[i*primes[j]]=ds[i]*dp[i],dp[i*primes[j]]=2; else {
is[i*primes[j]]=1,dp[i*primes[j]]=dp[i]+1;
break;
}
}
}
for(int i=2;i<maxn;++i) ds[i]*=dp[i];
}
};
#define maxm 10000005
struct linear_inverse{
long long inv[maxm];
inline void mx(int n,long long m){
inv[1]=1;
for(int i=1;i<=n;++i){
inv[i]=((-(m/i)*inv[(int)(m%i)])%m+m)%m;
}
}
};
typedef unsigned long long ll;
ll dev(ll n){//count number of divisors O(sqrt(n))
ll res=1,t=2,p;
while(n*n>=t){
p=1;
while(!(n%t)){
n/=t;
++p;
}
res*=p;
++t;
}
if(n!=1) res<<=1;
return res;
}
ll sigma(ll n){//count sum of divisors O(sqrt(n))
ll res=1,t=2,tp;
while(n*n>=t){
tp=t;
while(!(n%t)){
n/=t;
tp*=t;
}
res*=(tp-1)/(t-1);
++t;
}
if(n!=1) res*=n+1;
return res;
}
//modmul O(1)
inline ll modmul(ll a,ll b,ll p){ return ((a*b-(ll)(((long double)a*b)/p)*p)%p+p)%p; }
inline ll modpow(ll a,ll e,ll p){//fast power O(log e)
ll q=1;
while(e){
if(e&1) q=modmul(q,a,p);
a=modmul(a,a,p);
e>>=1;
}
return q;
}
inline bool Miller_Rabin_Single(ll a,ll u,ll r,ll n){//primality test for (si-)prime u*2^r+1 base a
ll k=modpow(a,u,n),pre=k;
while(r--){
k=modmul(k,k,n);
if(k==1ll && pre!=1ll && pre!=n-1) return 0;
pre=k;
}
return k==1ll;
}
bool Miller_Rabin(ll n){//test primality
if(n==2 || n==3 || n==5 || n==7 || n==11) return 1;
if(!(n&1) || !(n%3) || !(n%5) || !(n%7) || !(n%11)) return 0;
ll u=n-1,r=0;
while(!(u&1)) u>>=1,++r;
if(!Miller_Rabin_Single(2,u,r,n)) return 0;
if(!Miller_Rabin_Single(1215,u,r,n)) return 0;
if(!Miller_Rabin_Single(34862,u,r,n)) return 0;
if(!Miller_Rabin_Single(574237825,u,r,n)) return 0;
return 1;
}
template<class T>inline T gcd(T a,T b){//gcd O(log n)
T c;
while(a){
c=b%a;
b=a,a=c;
}
return b;
}
ll Polard_rho(ll n,ll c,ll u){//factor long long O(n^(1/4))
ll i=1,k=2;
ll y=u,x0=u;
while(1){
++i;
x0=(modmul(x0,x0,n)+c)%n;
ll d=gcd(y-x0,n);
if(d!=1 && d!=n) return d;
if(y==x0) return n;
if(i==k) y=x0,k+=k;
}
}
#define ed 300005
#define mi 1333357
struct hashmap{//hashmap with O(1) clearing
int next[ed][4],h[mi],u,x;
inline void operator()(){
u=0,next[0][2]=-1,++x;
}
inline void operator()(long long n,int k){
int q=n%mi,t=h[q];
while(t && next[t][0]!=n && next[t][3]==x) t=next[t][1];
if(!t || next[t][3]!=x){
++u;
next[u][0]=n,next[u][1]=h[q],t=u,next[u][3]=x;
h[q]=u;
}
next[t][2]=k;
}
inline int operator[](long long n){
int q=n%mi,t=h[q];
while(t && next[t][0]!=n && next[t][3]==x) t=next[t][1];
if(next[t][3]!=x) return -1;
return next[t][2];
}
};
inline unsigned int sqrt(ll x){ return (unsigned int)sqrt((double)x*x); }
struct BSGS{//Finding discrete logarithm
hashmap q;
inline ll operator()(ll a,ll b,ll p){
q(),q(1,0);
int m=sqrt(p);
ll v=modpow(a,p-m-1,p),e=1;
fox(i,1,m){
e=modmul(a,e,p);
q(e,i);
}
fon(i,m){
ll j=q[b];
if(~j) return i*m+j;
b=modmul(b,v,p);
}
return -1;
}
} Baby_Step_Giant_Step;
struct _pext_euc{//Solving ax+by=1
ll x,y;
ll exgcd(ll a,ll b){
ll t=0,d=0;
if(b){
d=exgcd(b,a%b);
t=x;
x=y;
y=t-(a/b)*y;
return d;
}else{
x=1,y=0;
return a;
}
}
inline ll operator()(ll a,ll b){
return exgcd(a,b);
}
} Extended_Euclid;
ll inv_fast(ll a,ll p){//calculate inverse O(log n) with exgcd
Extended_Euclid(a,p);
return (Extended_Euclid.x%p+p)%p;
}
ll eular_phi(ll a){//calculate eular phi O(sqrt(n))
ll i=2,t,r=1;
while(i*i<=a){
if(a%i){ ++i;continue;}else{
t=i-1,a=a/i;
while(!(a%i)) a=a/i,t=t*i;
++i,r=r*t;
}
}
if(a) r=r*(a-1);
return r;
}
struct exBSGS{
ll operator()(ll a,ll b,ll p){
ll k=0,u,l=1,x=1,A=a,B=b,P=p,ans=0;
if(B==1) return 0;
if(A==B) return 1;
while((u=gcd(a,p))!=1){
if(b%u) return -1;
++k,l=a/u,b=b/u,p=p/u;
x=modmul(l,x,p);
if(x==b) ans=k;
}
ll y=inv_fast(x,p);
b=modmul(b,y,p);
if(!ans) ans=Baby_Step_Giant_Step(a,b,p);
a=A,b=B;
fox(i,2,k){
a=modmul(a,A,p);
if(a==b) return i;
}
return ans+k;
}
} extended_Baby_Step_Giant_Step;
ll least_primitive_root_for_prime(ll n){//O(g sqrt(n))
fox(i,2,n){
if(Baby_Step_Giant_Step(i,1,n)==n-1) return i;
}
return -1;
}
ll least_primitive_root(ll n){
ll p=eular_phi(n);
fox(i,2,n){
if(extended_Baby_Step_Giant_Step(i,1,n)==p) return i;
}
return -1;
}
struct Comb_Number_Small1{//O(mn)-O(1) p none
ll CC[2002][2002];
inline void init(int n,ll p){
CC[1][1]=1;
foxe(i,1,n){
foxe(j,1,i){
CC[i][j]=(CC[i-1][j-1]+CC[i-1][j])%p;
}
}
}
inline ll operator()(int n,int m){
return CC[n][m];
}
};
struct Comb_Number_Small2{//O(n)-O(1) p prime
linear_inverse li;
ll facn[maxm],infacn[maxm],pp;
inline void init(int n,ll p){
li.mx(n,p);
facn[1]=1,pp=p;
foxe(i,2,n) facn[i]=modmul(facn[i-1],i,p),infacn[i]=modmul(infacn[i-1],li.inv[i],p);
}
inline ll operator()(int n,int m){
if(m>n) return 0;
ll a=modmul(infacn[m],infacn[n-m],pp);
return modmul(facn[n],a,pp);
}
};
struct Comb_Number_Lucas{
Comb_Number_Small2 b;
ll pp;
inline void init(ll n,ll p){
b.init((int)p,p);
pp=p;
}
inline ll operator()(int n,int m){
ll ans=1,kk;
while(m){
kk=b(n%pp,m%pp);
ans=modmul(kk,ans,pp);
if(!ans) return 0;
n/=pp,m/=pp;
}
return ans;
}
};
struct Comb_Number_factor{
linear_sieve s;
int count[2000010];
inline void init(){
s();
}
inline int calcp(int n,int p){
int res=0,pp=p;
while(n>=pp) res+=n/pp,pp=p*pp;
return res;
}
inline ll operator()(int n,int m,ll p){
int k=m-n;
for(int i=0;s.primes[i]<=n;++i) count[i]=calcp(n,s.primes[i]);
for(int i=0;s.primes[i]<=m;++i) count[i]-=calcp(m,s.primes[i]);
for(int i=0;s.primes[i]<=k;++i) count[i]-=calcp(k,s.primes[i]);
ll res=1,pq;
for(int i=0;s.primes[i]<=n;++i){
pq=modpow(s.primes[i],count[i],p);
res=modmul(res,pq,p);
}
return res;
}
};
#define crtn 400005
struct CRT{
ll de[crtn],nn[crtn];//product of de should be within range<long long>()
inline ll operator()(int n){
ll M=1,ans=0;
fon(i,n) M*=de[n];
fon(i,n){
ll t=M/de[n],inv=inv_fast(t,de[n]);
ans=(ans+t*inv*nn[n])%M;
}
return (ans+M)%M;
}
};
struct _solve_linear_congruent_equations{
ll de[crtn],nn[crtn];
inline void single(ll &x,ll &y,ll c,ll d){
ll a=x,b=y;
x=gcd(b,d);
y=(ll)(((long double)a*b)/x);//lcm a,b
ll t=inv_fast(b,d),t2=c-a;
x=modmul(t,t2,y);
}
inline ll operator()(int n){
fox(i,1,n) single(nn[0],de[0],nn[i],de[i]);
return nn[0];
}
};
ll lcm(ll a,ll b){
ll t=gcd(a,b);
return (ll)(((long double)a*b)/t);
}
}
int main(){
}
