cf449D. Jzzhu and Numbers(容斥原理 高维前缀和)

#include<bits/stdc++.h>
#define Pair pair<int, int>
#define MP make_pair
#define fi first
#define se second 
using namespace std;
const int MAXN = 3e6 + 10, mod = 1e9 + 7, B = 20;
inline int read() {
    char c = getchar(); int x = 0, f = 1;
    while(c < '0' || c > '9') {if(c == '-') f = -1; c = getchar();}
    while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
    return x * f;
}
int N, a[MAXN], bit[65537], f[MAXN];
int add(int &x, int y) {
    if(x + y < 0) x = x + y + mod;
    else x = (x + y >= mod ? x + y - mod : x + y);
}
int mul(int x, int y) {
    return 1ll * x * y % mod;
}
int fp(int a, int p) {
    int base = 1;
    while(p) {
        if(p & 1) base = mul(base, a);
        a = mul(a, a); p >>= 1;
    }
    return base;
}
int get1(int x) {
//  return __builtin_popcount(x);
    return bit[x & 65535] + bit[x >> 16];
}
int main() {
    for(int i = 1; i <= 65536; i++) bit[i] = bit[i >> 1] + (i & 1);
    N = read();
    for(int i = 1; i <= N; i++) a[i] = read(), f[a[i]]++;
    int Lim = (1 << B) - 1, ans = 0;
    for(int i = 0; i <= 20; i++)
        for(int sta = 0; sta <= Lim; sta++) 
            if(!(sta & (1 << i))) add(f[sta], f[sta | (1 << i)]);
    for(int sta = 0; sta <= Lim; sta++) {
        int k = (get1(sta) & 1) ? -1 : 1;
        add(ans, mul(k, fp(2, f[sta])));
    }
    cout << ans;
    return 0;
}