#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <complex>
#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
typedef complex<double> cp; //complex库
const double PI = acos(-1);
void fft(cp *a,int n,int flag) //作用：求出a的点值表达，存进a
{
int i;
cp a0[n/2+1],a1[n/2+1];
if(n==1) return;
cp w_n(cos(2*PI/n),sin(flag*2*PI/n)); //flag=1:求值 flag=2:插值
cp w(1,0);
for(i=0; i<n/2; i++) a0[i]=a[i*2],a1[i]=a[i*2+1]; //分治
fft(a0,n/2,flag);
fft(a1,n/2,flag);
for(i=0; i<n/2; i++)
{
a[i]=a0[i]+w*a1[i];
a[i+n/2]=a0[i]-w*a1[i];
w=w*w_n; //递推单位复数根
}
}
cp x[300005]= {0},y[300005]= {0};
char arr1[100005], arr2[100005];
int ans[200005];
int main()
{
while(~scanf("%s%s", arr1, arr2))
{
for(int i=0; i<300005; i++) x[i]=cp(0, 0);
for(int i=0; i<300005; i++) y[i]=cp(0, 0);
int n, m, i;
n=strlen(arr1)-1;
m=strlen(arr2)-1;
for(i=0; i<=n; i++) x[i]=cp(arr1[n-i]-'0', 0);
for(i=0; i<=m; i++) y[i]=cp(arr2[m-i]-'0', 0);
m+=n;
for(n=1; n<=m; n=n*2);
fft(x,n,1); //求值
fft(y,n,1); //求值
for(i=0; i<n; i++) x[i]=x[i]*y[i]; //点值乘法
fft(x,n,-1); //插值
memset(ans, 0, sizeof(ans));
for(i=0; i<n || ans[i]; i++)
{
ans[i]+=(x[i].real()/n+0.5);
ans[i+1]+=(ans[i]/10);
ans[i]%=10;
}
while(i>0 && !ans[i])i--;
for(; i>=0; i--) printf("%d", ans[i]);
printf("\n");
}
return 0;
}
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <complex>
#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
const double PI = acos(-1);
struct Complex
{
double real, image;
Complex(double real=0.0, double image=0.0): real(real), image(image) {}
Complex operator +(const Complex &b)
{
return Complex(real+b.real,image+b.image);
}
Complex operator -(const Complex &b)
{
return Complex(real-b.real,image-b.image);
}
Complex operator *(const Complex &b)
{
return Complex(real*b.real-image*b.image,real*b.image+image*b.real);
}
};
Complex x[300005]= {0},y[300005]= {0};
char arr1[100005], arr2[100005];
int ans[200005];
int n, m;
void reverse(Complex a[],int n) //对长度为的复数序列a进行DFT和IDFT之前必要的反转变换操作(比特反转),n一定是2的幂次
{
for(int i=1,j=n/2,k; i<n-1; i++)
{
if(i<j) swap(a[i],a[j]);
k=n/2;
while(j>=k)
{
j-=k;
k/=2;
}
if(j<k) j+=k;
}
}
void fft(Complex *a,int n,int flag) //flag=1是求值，flag=-1是插值
{
reverse(a,n);
for(int i=1; i<n; i<<=1) //i=该层的相邻结点之间编号之差，logn次迭代模拟，自底向上
{
Complex wn=Complex(cos(PI/i),flag*sin(PI/i));
for(int j=0; j<n; j+=(i<<1)) //编号为j的结点
{
Complex w=Complex(1,0);
for(int k=0; k<i; k++,w=w*wn)
{
Complex x=a[j+k],y=w*a[j+k+i]; //x和y是当前节点左右递归下去后得到的fft值，当然，y(右儿子，奇数项)的fft值要乘上一个w
a[j+k]=x+y;
a[j+k+i]=x-y;
}
}
}
if(flag==-1) //如果是插值，还得在前面加个1/n的系数
for(int i=0; i<n; i++)
a[i].real/=n;
}
void Fast_Fourier_Transform(char *arr1, char *arr2)
{
int i;
n=strlen(arr1)-1;
m=strlen(arr2)-1;
for(i=0; i<=n; i++) x[i]=Complex(arr1[n-i]-'0', 0);
for(i=0; i<=m; i++) y[i]=Complex(arr2[m-i]-'0', 0);
m+=n;
for(n=1; n<=m; n=n*2);
fft(x,n,1); //求值
fft(y,n,1); //求值
for(i=0; i<n; i++) x[i]=x[i]*y[i]; //点值乘法
fft(x,n,-1); //插值
}
int main()
{
while(~scanf("%s%s", arr1, arr2))
{
int i;
for(i=0; i<300005; i++) x[i]=Complex(0, 0);
for(i=0; i<300005; i++) y[i]=Complex(0, 0);
Fast_Fourier_Transform(arr1, arr2);
memset(ans, 0, sizeof(ans));
for(i=0; i<n || ans[i]; i++)
{
ans[i]+=(x[i].real+0.5);
ans[i+1]+=(ans[i]/10);
ans[i]%=10;
}
while(i>0 && !ans[i])i--;
for(; i>=0; i--) printf("%d", ans[i]);
printf("\n");
}
return 0;
}
