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

typedef long long LL;

const int N = 30, mod = 1e9 + 7;

LL p[N];
LL down = 1;    

int qmi(int a, int k) {
    int ret = 1;
    while (k) {
        if (k & 1) ret = 1ll * ret * a % mod;
        a = 1ll * a * a % mod;
        k >>= 1;
    }
    return ret;
}

int C(LL a, LL b) {
    if (a < b) return 0;
    int up = 1; 
    for (LL i = a; i > a - b; i--) {
        up = i % mod * up % mod;
    }
    return up * down % mod; 
}

int main() {
    LL n, m;
    scanf("%lld %lld", &n, &m);
    for (int i = 0; i < n; i++) {
        scanf("%lld", p + i);
    }
    for (int i = 1; i < n; i++) {
        down = down * i % mod;
    }
    down = qmi(down, mod - 2);  
    int ret = C(m + n - 1, n - 1);
    for (int i = 1; i < 1 << n; i++) {
        LL a = m + n - 1, b = n - 1, cnt = 0;
        for (int j = 0; j < n; j++) {
            if (i >> j & 1) a -= p[j] + 1, cnt ^= 1;
        }
        if (cnt) ret = (ret - C(a, b)) % mod;
        else ret = (ret + C(a, b)) % mod;
    }
    printf("%d", (ret + mod) % mod);

    return 0;
}