#include <cstdio>
#include <cstring>
#include <malloc.h>
#define radix (1u<<28)
#define drdx (radix-1)
#define max_size 100000000u
typedef unsigned int qt;
typedef qt ul;
inline qt max(qt a,qt b){ return ((-((a-b)>>31))&(b-a))+a; }
inline qt min(qt a,qt b){ return ((-((a-b)>>31))&(a-b))+b; }
struct bigint{
qt *d;
qt s,l;
};
template<class T> inline void alc ( T* &p, ul l ){
p=(T*)malloc( l * sizeof(T) );
}
template<class T> inline void palc( T* f, T* &t, ul l, ul a ){
if(t) free(t),t=NULL;
alc( t, a );
memcpy( t, f, sizeof(T) * l );
memset( t+l, 0, sizeof(T) * (a-l) );
}
template<class T> inline void palc( T* &t, ul a ){
if(t) free(t),t=NULL;
alc( t, a );
memset( t, 0, sizeof(T) * a );
}
inline void larger(bigint& i){
qt *p=NULL;
palc(i.d,p,i.l,i.s<<1);
i.s<<=1;
free(i.d);
i.d=p;
}
inline qt add(bigint& a,bigint& b){//return carry
qt l=max(a.l,b.l),car=0;
while(a.s<l) larger(a);
a.l=l; qt i=0;
for(;i<l;++i){
if(b.l==i) break;
a.d[i]+=b.d[i]+car;
car=a.d[i]>>28;
a.d[i]&=drdx;
}
for(;i<l;++i){
a.d[i]+=car;
car=a.d[i]>>28;
a.d[i]&=drdx;
}
return car;
}
inline qt sub(bigint& a,bigint& b){//return borrow
qt l=max(a.l,b.l),bor=0;
while(a.s<l) larger(a);
a.l=l; qt i=0;
for(;i<l;++i){
if(b.l==i) break;
a.d[i]-=b.d[i]+bor;
bor=a.d[i]>>31;
a.d[i]+=(-bor)&radix;
}
for(;i<l;++i){
a.d[i]-=bor;
bor=a.d[i]>>31;
a.d[i]+=(-bor)&radix;
}
if(!bor){
while(!a.d[--a.l]);
++a.l;
}
return bor;
}
inline qt mul_basecase(bigint& c,bigint& a,bigint& b){//return carry, c=c+a*b
qt l=a.l+b.l,car=0;
while(c.s<l) larger(c);
for(qt i=0;i<a.l;++i) for(qt j=0,p=i;j<b.l;++j,++p) {
long long nk=(long long)a.d[i]*b.d[j]+c.d[p];
c.d[p]=nk&drdx;
c.d[p+1]+=nk>>28;
c.d[p+2]+=c.d[p+1]>>28;
c.d[p+1]&=drdx;
}
if(c.d[l-1]) c.l=l; else c.l=l-1;
return c.d[l-1]>>28;
}
inline qt mul_limb(bigint& a,qt limb){
qt car=0;
for(int i=0;i<a.l;++i){
long long nk=(long long)a.d[i]*limb+car;
a.d[i]=nk&drdx;
car=nk>>28;
}
return car;
}
inline qt sqr_basecase(bigint& c,bigint& a){//a speed-up of roughly a half
qt l=a.l+a.l,car=0;
while(c.s<l) larger(c);
for(qt i=0;i<a.l;++i){
qt p=i<<1;
long long nk=(long long)a.d[i]*a.d[i]+c.d[p];
c.d[p]=nk&drdx;
c.d[p+1]+=nk>>28;
c.d[p+2]+=c.d[p+1]>>28;
c.d[p+1]&=drdx;
++p;
for(qt j=i+1;j<a.l;++j,++p) {
long long nk=((long long)a.d[i]*(a.d[j])<<1)+c.d[p];
c.d[p]=nk&drdx;
c.d[p+1]+=nk>>28;
c.d[p+2]+=c.d[p+1]>>28;
c.d[p+1]&=drdx;
}
}
if(c.d[l-1]) c.l=l; else c.l=l-1;
return c.d[l-1]>>28;
}
inline qt mul(bigint& c,bigint& a,bigint& b); //automatically select the algorithm used
inline qt sqr(bigint& c,bigint& a);
inline qt div(bigint& a,bigint& b,bigint& r);
inline bigint empty(qt ofsize){
bigint vt;
vt.l=1; vt.s=ofsize;
vt.d=NULL;
palc(vt.d,vt.s);
return vt;
}
inline bigint copy(bigint p){//obtaining a copy from p
bigint vt=p;
qt* t;
palc(vt.d,t,vt.l,vt.s);
vt.d=t;
return vt;
}
inline void pushCarry(bigint& p,qt car){
if(p.l==p.s) larger(p);
p.d[p.l++]=car;
}
inline void getBigInt_tm1(bigint& p){
scanf("%u",&p.l);
while(p.s<p.l) larger(p);
for(qt i=0;i<p.l;++i) scanf("%u",&p.d[i]);
}
inline void printBigInt_tm1(bigint& p){
printf("Length of BigInt: %u\n Size of BigInt: %u int(s)\n",p.l,p.s);
printf(" %-10d * 2^%-4d",p.d[0],0);
for(qt i=1,v=28;i<p.l;(++i)&3?0:putchar('\n'),v+=28) printf(" + %-10d * 2^%-4d",p.d[i],v);
putchar('\n');
}
inline void makeEmpty(bigint& n){
memset(n.d,0,sizeof(qt)*n.l);
n.l=1;
}
inline void makeIdentity(bigint& n){
memset(n.d,0,sizeof(qt)*n.l);
n.d[0]=1;
n.l=1;
}
inline void transfer(bigint& dest,bigint& src){
while(dest.s<src.l) larger(dest);
memcpy(dest.d,src.d,sizeof(qt)*src.l);
dest.l=src.l;
}
//fast powering error code: -1: result too large
inline int fastPower(bigint& n,qt now){
qt size=n.l*now;
if(size>max_size) return -1;
bigint cs[2],cx;
qt fx=0;
cs[0]=empty(size),cs[1]=empty(size),cx=empty(size);
transfer(cs[0],n);
for(;now;(now>>=1),fx=1-fx){
makeEmpty(cx);
if(now&1){
mul(cx,cs[fx],n);
transfer(n,cx);
}
makeEmpty(cs[1-fx]);
sqr(cs[1-fx],cs[fx]);
}
return 0;
}
inline qt karatsuba_mul(bigint& c,bigint& a,bigint& b);
inline qt toom_3_mul(bigint& c,bigint& a,bigint& b);
inline qt toom_4_mul(bigint& c,bigint& a,bigint& b);
inline qt ss_mul(bigint& c,bigint& a,bigint& b);
////////////Classical part ends.
