FWT

$FFT:$ $C_k={\sum }_{i+j=k}{A}_i\ast B_j$
$FWT:$ $C_k={\sum }_{i\oplus j=k}{A}_i\ast B_j$

#include
using namespace std;
const int N = 1 << 17, P = 998244353, inv_2 = 499122177;
inline int add(int a, int b){
     return a + b >= P ? a + b - P : a + b;}
inline int sub(int a, int b){
     return a - b < 0 ? a - b + P : a - b;}
inline int mul(int a, int b){
     return 1ll * a * b - 1ll * a * b / P * P;}
int a[N], b[N], c[N];

inline int read()
{
     
    int x = 0, f = 1; char ch = getchar();
    for (; ch < '0' || ch > '9'; ch = getchar()) if (ch == '-') f = -1;
    for (; ch >= '0' && ch <= '9'; ch = getchar()) x = (x << 1) + (x << 3) + ch - '0';
    return x * f;
}

inline void FWTor(int *a, int n, int t)
{
     
    for (register int i = 1; i < n; i <<= 1)
        for (register int j = 0; j < n; j += (i << 1))
            for (register int k = 0; k < i; ++k)
                if (~t) a[i + j + k] = add(a[i + j + k], a[j + k]);
                    else a[i + j + k] = sub(a[i + j + k], a[j + k]);
}

inline void FWTand(int *a, int n, int t)
{
     
    for (register int i = 1; i < n; i <<= 1)
        for (register int j = 0; j < n; j += (i << 1))
            for (register int k = 0; k < i; ++k)
                if (~t) a[j + k] = add(a[j + k], a[i + j + k]);
                    else a[j + k] = sub(a[j + k], a[i + j + k]);
}

inline void FWTxor(int *a, int n, int t)
{
     
    for (register int i = 1; i < n; i <<= 1)
        for (register int j = 0; j < n; j += (i << 1))
            for (register int k = 0; k < i; ++k)
            {
     
                int x = a[j + k], y = a[i + j + k];
                a[j + k] = add(x, y);
                a[i + j + k] = sub(x, y);
                if (!~t) 
                    a[j + k] = mul(a[j + k], inv_2),
                    a[i + j + k] = mul(a[i + j + k], inv_2);
            }
}

int main()
{
     
    int n = read(), m = 1 << n; 
    for (register int i = 0; i < m; ++i) a[i] = read();
    for (register int i = 0; i < m; ++i) b[i] = read();
    
    FWTor(a, m, 1); FWTor(b, m, 1);
    for (register int i = 0; i < m; ++i) c[i] = mul(a[i], b[i]);
    FWTor(a, m, -1); FWTor(b, m, -1); FWTor(c, m, -1);
    for (register int i = 0; i < m; ++i) printf("%d ", c[i]); puts("");
    
    FWTand(a, m, 1); FWTand(b, m, 1);
    for (register int i = 0; i < m; ++i) c[i] = mul(a[i], b[i]);
    FWTand(a, m, -1); FWTand(b, m, -1); FWTand(c, m, -1);
    for (register int i = 0; i < m; ++i) printf("%d ", c[i]); puts("");
    
    FWTxor(a, m, 1); FWTxor(b, m, 1);
    for (register int i = 0; i < m; ++i) c[i] = mul(a[i], b[i]);
    FWTxor(a, m, -1); FWTxor(b, m, -1); FWTxor(c, m, -1);
    for (register int i = 0; i < m; ++i) printf("%d ", c[i]); puts("");
    
    return 0;
}

void FWT(LL *a,int n)
{
     
    for (int i=1;i<n;i<<=1)
     for (int p1=i<<1,j=0;j<n;j+=p1)
      for (int k=0;k<i;k++) {
     
        LL x=a[j+k]; LL y=a[j+k+i];
        a[j+k]=(x+y)%p; 
        a[j+k+i]=(x-y+p)%p;
        //xor: a[j+k]=x+y,a[j+k+i]=x-y
        //and: a[j+k]=x+y
        //or : a[j+k+i]=x+y
      }
}
void UFWT(LL *a,int n)
{
     
    for (int i=1;i<n;i<<=1)
     for (int p1=i<<1,j=0;j<n;j+=p1)
      for (int k=0;k<i;k++){
     
        LL x=a[j+k]; LL y=a[j+k+i];
        a[j+k]=(x+y)%p*ret%p;
        a[j+k+i]=((x-y)*ret%p+p)%p;
        //xor: a[j+k]=(x+y)/2,a[j+k+i]=(x-y)/2
        //and: a[j+k]=x-y
        //or : a[j+k+i]=y-x
      }
}
void solve(LL *a,LL *b,int n)
{
     
    FWT(a,n); FWT(b,n);
    for (int i=0;i<n;i++) a[i]=a[i]*b[i]%p;
    UFWT(a,n);
}