Problem: Devu wants to decorate his garden with flowers. He has purchased n boxes, where the i-th box contains fi flowers. All flowers in a single box are of the same color (hence they are indistinguishable). Also, no two boxes have flowers of the same color.

Now Devu wants to select exactly s flowers from the boxes to decorate his garden. Devu would like to know, in how many different ways can he select the flowers from each box? Since this number may be very large, he asks you to find the number modulo (109 + 7). 

Devu considers two ways different if there is at least one box from which different number of flowers are selected in these two ways.

Input

The first line of input contains two space-separated integers n and s (1 ≤ n ≤ 20, 0 ≤ s ≤ 1014).

The second line contains n space-separated integers f1, f2, ... fn (0 ≤ fi ≤ 1012).

Output

Output a single integer — the number of ways in which Devu can select the flowers modulo (109 + 7).

Examples

Input

2 3
1 3


Output

2


Input

2 4
2 2


Output

1


Input

3 5
1 3 2


Output

3

Note

Sample 1. There are two ways of selecting 3 flowers: {1, 2} and {0, 3}.

Sample 2. There is only one way of selecting 4 flowers: {2, 2}.

Sample 3. There are three ways of selecting 5 flowers: {1, 2, 2}, {0, 3, 2}, and {1, 3, 1}.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
int64_t calc_inverse(int64_t x) {
  int64_t p1, p2;
  std::function<void(int64_t, int64_t, int64_t, int64_t, int64_t, int64_t)>
      gcd = [&](int64_t a, int64_t ma, int64_t na, int64_t b, int64_t mb,
                int64_t nb) {
        if (b != 0) {
          int64_t q = a / b;
          int64_t c = a % b;
          int64_t mc = ma - q * mb;
          int64_t nc = na - q * nb;
          gcd(b, mb, nb, c, mc, nc);
        } else {
          p1 = ma;
          p2 = na;
        }
      };
  gcd(1000000007, 1, 0, x, 0, 1);
  int64_t inverse = p2 % 1000000007;
  if (inverse < 0) inverse += 1000000007;
  return inverse;
}
int main() {
  int64_t n, s, f[20];
  scanf("%" SCNd64 " %" SCNd64, &n, &s);
  for (int64_t *ptr = f; ptr < f + n; ptr++) scanf("%" SCNd64, ptr);
  int64_t factorial = 1;
  for (int64_t i = 2; i <= n - 1; i++) factorial = factorial * i % 1000000007;
  int64_t inverse = calc_inverse(factorial);
  auto comb_with_rep = [&](int64_t k) {
    int64_t result = 1;
    for (int64_t i = n + k - 1; i > k; i--)
      result = result * (i % 1000000007) % 1000000007;
    result = result * inverse % 1000000007;
    return result;
  };
  int64_t r = s;
  int64_t sign = 1;
  int64_t count = comb_with_rep(r);
  for (int prev_gray = 0, cnt = 1; cnt < (1 << n); cnt++) {
    sign = -sign;
    int gray = cnt ^ (cnt >> 1);
    int altered_bit = prev_gray ^ gray;
    int index = __builtin_ctz(altered_bit);
    if (gray & altered_bit)
      r -= f[index] + 1;
    else
      r += f[index] + 1;
    if (r >= 0) {
      count = (count + sign * comb_with_rep(r)) % 1000000007;
      if (count < 0) count += 1000000007;
    }
    prev_gray = gray;
  }
  printf("%" PRId64 "\n", count);
  return 0;
}