CF541E.cpp

#include <bits/stdc++.h>
using namespace std;

#define int long long
const int N = 22, P = 1e9+7;
int f[N], s;
int n;

map<int, int> F;

int qpow(int a, int k) {
    int res = 1;
    while (k) {
        if (k & 1) res = res * a % P;
        a = a * a % P;
        k >>= 1;
    }
    return res;
}

int C(int m, int n) {
    int res = 1;
    for (int j = 0; j < n; j++) res = res * ((m - j) % P) % P;
    int fact = 1;
    for (int j = 1; j <= n; j++) fact = fact * j % P;
    return res * qpow(fact, P-2) % P;
}

signed main() {
    ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
    cin >> n >> s;
    for (int i = 0; i < n; i++) cin >> f[i];

    for (int S = 0; S < 1 << n; S++) {
        int idx = 0, val = 1;
        for (int i = 0; i < n; i++) {
            if (S >> i & 1) {
                idx += f[i] + 1;
                val = -val;
            }
        }
        F[idx] = (F[idx] + P + val) % P;
    }

    int ans = 0;
    for (const auto& [i, fi]: F) {
        // [x^s] F(x) / (1-x)^n
        int m = s - i;
        if (m < 0) continue;
        ans = (ans + fi * C(m+n-1, n-1)) % P;
    }
    cout << ans << '\n';
    return 0;
}