[cogs 2190]花样游戏

FWT

#define MAXN 200010
#include  

using namespace std;
typedef long long ll;
const int md = 1e9 + 7, inv2 = 500000004;

int power_mod(int a, int b = md - 2) {
    int ret = 1;
    while(b > 0) {
        if(b & 1) ret = (ll)ret * a % md;
        b >>= 1;
        a = (ll)a * a % md;
    }return ret;
}

void fwt(int* A, int n) {
    for(int k = 1 ; k <= n ; k <<= 1) {
        int t = k>>1;
        for(int i = 0 ; i <= n ; i += k) {
            for(int j = 0 ; j < t ; j ++) {
                int x = A[i+j], y = A[i+j+t];
                A[i+j] = (x + y) % md;
                A[i+j+t] = (x - y) % md;
            }
        }
    }
}

void ifwt(int* A, int n) {
    for(int k = 1 ; k <= n ; k <<= 1) {
        int t = k>>1;
        for(int i = 0 ; i <= n ; i += k) {
            for(int j = 0 ; j < t ; j ++) {
                int x = A[i+j], y = A[i+j+t];
                A[i+j] = (ll)(x + y) * inv2 % md;
                A[i+j+t] = (ll)(x - y) * inv2 % md;
            }
        }
    }
}

int f[MAXN], p[MAXN], primes, n, m;
bool vis[MAXN];

int main() {
    freopen("srmnim.in", "r", stdin);
    freopen("srmnim.out", "w", stdout);
    n = 60000;
    for(int i = 2 ; i <= n ; ++ i) {
        if(!vis[i]) p[++ primes] = i;
        for(int j = 1 ; j <= primes ; ++ j) {
            if(1ll * i * p[j] > n)break;
            vis[i * p[j]] = true;
            if(i % p[j] == 0)break;
        }
    }

    while(~ scanf("%d%d", &n, &m)) {
        int N = 1;
        for( ; N <= m ; N <<= 1);
        for(int i = 0 ; i < N ; ++ i)f[i] = 0;
        for(int i = 1 ; p[i] <= m ; ++ i)
            f[p[i]] = 1;
        fwt(f, N);
        for(int i = 0 ; i < N ; ++ i)
            f[i] = power_mod(f[i], n);
        ifwt(f, N);
        printf("%d\n", (f[0]+md)%md);
    }
    return 0;
}