【代码】

#include <bits/stdc++.h>
#define For(i, a, b) for(register int i = (a); i <= (b); ++i)
#define Rof(i, a, b) for(register int i = (a); i >= (b); --i)
#define INF 0x3f3f3f3f
#define LL long long
#define Mod 1000000007
using namespace std;
int N;
LL A[21], M, Ans, Inv[21], Pos = 1;
LL Pow(LL a, int k) {
    LL Ret = 1;
    for(;k ; k >>= 1, a = a * a % Mod) if(k & 1) Ret = Ret * a % Mod;
    return Ret;
} 
LL C(LL x, int y) {
    if(x < 0 || y < 0 || x < y) return 0;
    if(x == y || y == 0) return 1;
    x %= Mod;
    LL Ret = 1;
    For(i, 0, y - 1) Ret = Ret * (x - i) % Mod;
    return Ret * Pos % Mod;
}
int main() {
    scanf("%d%lld", &N, &M); For(i, 1, N) scanf("%lld", &A[i]);
    For(i, 1, N - 1) Inv[i] = Pow(i, Mod - 2), Pos = Pos * Inv[i] % Mod;
    Ans = C(N + M - 1, N - 1);
    For(Sta, 1, Pow(2, N) - 1) {
        LL t = 1, k = 0;
        For(i, 1, N) if(Sta >> (i - 1) & 1) t += 1 + A[i], ++k;
        if(k & 1) Ans = (Ans - C(N + M - t, N - 1)) % Mod;
        else Ans = (Ans + C(N + M - t, N - 1)) % Mod;
    }
    printf("%lld\n", (Ans + Mod) % Mod);
    return 0;
}