https://www.cnblogs.com/RabbitHu/p/9182047.html

　　完全沒有學證明的慾望因為這個實在太好寫了而且FFT就算學過也忘得差不多了只會寫板子

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<cstdlib>
#include<algorithm>
using namespace std;
#define N (1<<17)
#define P 998244353
#define
 
 inv2 499122177
int read()
{
    int x=0,f=1;char c=getchar();
    while (c<'0'||c>'9') {if (c=='-') f=-1;c=getchar();}
    while (c>='0'&&c<='9') x=(x<<1)+(x<<3)+(c^48),c=getchar();
    return x*f;
}
int n,a[N],b[N],f[N],g[N];
void OR(int *a,int n,int op)
{
    for (int
 
 i=2;i<=n;i<<=1)
        for (int j=0;j<n;j+=i)
            for (int k=j;k<j+(i>>1);k++)
            {
                int x=a[k],y=a[k+(i>>1)];
                if (op==0) a[k]=x,a[k+(i>>1)]=(x+y)%P;
                else a[k]=x,a[k+(i>>1)]=(y-x+P)%P;
            }
}
 
void AND(int *a,int n,int op)
{
    for (int i=2;i<=n;i<<=1)
        for (int j=0;j<n;j+=i)
            for (int k=j;k<j+(i>>1);k++)
            {
                int x=a[k],y=a[k+(i>>1)];
                if (op==0) a[k]=(x+y)%P,a[k+(i>>1)]=y;
                else a[k]=(x-y+P)%P,a[k+(i>>1)]=y;
            }
}
void XOR(int *a,int n,int op)
{
    for (int i=2;i<=n;i<<=1)
        for (int j=0;j<n;j+=i)
            for (int k=j;k<j+(i>>1);k++)
            {
                int x=a[k],y=a[k+(i>>1)];
                a[k]=(x+y)%P,a[k+(i>>1)]=(x-y+P)%P;
                if (op==1) a[k]=1ll*a[k]*inv2%P,a[k+(i>>1)]=1ll*a[k+(i>>1)]*inv2%P;
            }
}
void FWT(int *a,int *b,int n,int op)
{
    if (op==0) OR(a,n,0),OR(b,n,0);
    else if (op==1) AND(a,n,0),AND(b,n,0);
    else if (op==2) XOR(a,n,0),XOR(b,n,0);
    for (int i=0;i<n;i++) a[i]=1ll*a[i]*b[i]%P;
    if (op==0) OR(a,n,1);
    else if (op==1) AND(a,n,1);
    else if (op==2) XOR(a,n,1);
    for (int i=0;i<n;i++) printf("%d ",f[i]);cout<<endl;
}
int main()
{
    freopen("FWT.in","r",stdin);
    freopen("FWT.out","w",stdout);
    n=1<<read();
    for (int i=0;i<n;i++) a[i]=read();
    for (int i=0;i<n;i++) b[i]=read();
    memcpy(f,a,sizeof(f));memcpy(g,b,sizeof(g));
    FWT(f,g,n,0);
    memcpy(f,a,sizeof(f));memcpy(g,b,sizeof(g));
    FWT(f,g,n,1);
    memcpy(f,a,sizeof(f));memcpy(g,b,sizeof(g));
    FWT(f,g,n,2);
    return 0;
}