#include <bits/stdc++.h>
using namespace std;
const int mod = 1000000007;
long long a[22], m, ans = 0, inv[22], n;
int qmi(int x, int y) {
  int c = 1;
  while (y) {
    if (y & 1) c = (long long)c * x % mod;
    x = (long long)x * x % mod;
    y >>= 1;
  }
  return c;
}
int C(long long y, int x) {
  if (y < 0 || x < 0 || y < x) return 0;
  y %= mod;
  if (y == 0 || x == 0) return 1;
  int ans = 1;
  for (int i = 0; i < x; i++) ans = (long long)ans * (y - i) % mod;
  for (int i = 1; i <= x; i++) ans = (long long)ans * inv[i] % mod;
  return ans;
}
int main() {
  for (int i = 1; i <= 20; i++) inv[i] = qmi(i, mod - 2);
  cin >> n >> m;
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int x = 0; x < 1 << n; x++) {
    if (x == 0) {
      ans = (ans + C(n + m - 1, n - 1)) % mod;
    } else {
      long long t = n + m;
      int p = 0;
      for (int i = 0; i < n; i++)
        if (x >> i & 1) p++, t -= a[i + 1];
      t -= p + 1;
      if (p & 1)
        ans = (ans - C(t, n - 1)) % mod;
      else
        ans = (ans + C(t, n - 1)) % mod;
    }
  }
  cout << (ans + mod) % mod << endl;
  return 0;
}
