#include <bits/stdc++.h>
using namespace std;
const long long mod = 1e9 + 7;
int cnt[9];
long long num[9] = {0, 2, 3, 5, 7, 11, 13, 17, 19};
int cntt[9];
long long C(long long n, long long m) {
  if (m > n) return 0;
  if (m == n) return 1;
  long long temp = 1, x, y, j, i;
  for (i = 1; i <= 8; i++) cntt[i] = cnt[i];
  for (x = n - m + 1; x <= n; x++) {
    y = x;
    for (j = 8; j >= 1; j--) {
      while (cntt[j] && y % num[j] == 0) {
        cntt[j]--;
        y /= num[j];
      }
    }
    temp = (temp * (y % mod)) % mod;
  }
  return temp;
}
int main() {
  long long n, m, a[21], flag, tm, ans = 0, temp, j, k, i;
  cin >> n >> m;
  for (i = 1; i <= n; i++) cin >> a[i];
  memset(cnt, 0, sizeof(cnt));
  for (i = 2; i <= n - 1; i++) {
    j = i;
    for (k = 1; k <= 8; k++) {
      while (j % num[k] == 0) {
        j /= num[k];
        cnt[k]++;
      }
    }
  }
  for (i = 0; i < (1 << n); i++) {
    tm = m + n - 1;
    flag = 0;
    for (j = 0; j <= n - 1; j++)
      if ((i >> j) % 2 == 1) {
        flag++;
        tm -= a[j + 1] + 1;
      }
    temp = C(tm, n - 1);
    if (flag % 2)
      ans += mod - temp;
    else
      ans += temp;
    ans %= mod;
  }
  cout << ans << endl;
  return 0;
}
