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FFT.cpp
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FFT.cpp
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#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
struct Complex{
double r,i;
Complex(double r,double i):r(r),i(i){}
Complex(){}
inline Complex operator + ( const Complex& rhs ) const {
return Complex ( r + rhs.r, i + rhs.i ) ;
}
inline Complex operator - ( const Complex& rhs ) const {
return Complex ( r - rhs.r, i - rhs.i ) ;
}
inline Complex operator * ( const Complex& rhs ) const {
return Complex ( r * rhs.r - i * rhs.i, r * rhs.i + i * rhs.r ) ;
}
inline void operator /= ( const double& x ) {
r /= x, i /= x ;
}
inline void operator *= ( const Complex& rhs ) {
*this = Complex ( r * rhs.r - i * rhs.i, r * rhs.i + i * rhs.r ) ;
}
inline void operator += ( const Complex& rhs ) {
r += rhs.r, i += rhs.i ;
}
};
const int maxn=4e6+6;
#define PI 3.14159265354
int pos[maxn];
void init ( const int& n ) {
for ( int i = 0 ,j=0; i < n ; ++ i ) {
pos[i]=j;for (int l = n >> 1; (j ^= l) < l; l >>= 1);
}
}
void transform ( Complex *a, const int& n, bool inverse ) {
for ( int i = 0; i < n ; ++ i ){
if (i > pos[i]) std ::swap(a[i], a[pos[i]]);
}
for ( int l = 2 ; l <= n ; l <<= 1 ) {
int m = l / 2;Complex omega={cos(2*PI/l),inverse?-sin(2*PI/l):sin(2*PI/l)};
for ( Complex *p = a ; p != a + n ; p += l ) {
Complex x={1,0};
for ( int i = 0 ; i < m ; ++ i ,x *= omega) {
Complex t = x * p [m + i] ;
p [m + i] = p [i] - t ;p [i] += t ;
}
}
}
}
void dft ( Complex *a, const int& n ) {
transform ( a, n, 0 ) ;
}
void idft ( Complex *a, const int& n ) {
transform ( a, n, 1) ;
for ( int i = 0 ; i < n ; ++ i ) a [i] /= n ;
}
Complex A[maxn],B[maxn],C[maxn];
void FFT(int n,int m) {// len(A),len(B)
int cnt=1;while(cnt<=(n+m)) cnt<<=1;
init(cnt);dft(A,cnt);dft(B,cnt);
for(int i=0;i<cnt;i++) C[i]=A[i]*B[i];
idft(C,cnt);
for(int i=0;i<=n+m;i++) C[i].r=ll(C[i].r+0.01);
}
int main(){
int n,m,tem;cin>>n>>m;
for(int i=0;i<=n;i++) scanf("%d",&tem),A[i].r=tem;
for(int i=0;i<=m;i++) scanf("%d",&tem),B[i].r=tem;
FFT(n,m);
for(int i=0;i<=n+m;i++) printf("%lld ",ll(C[i].r));cout<<"\n";
}