#include <bits/stdc++.h>
using namespace std;
const long long mod = 1e9 + 7;
long long m, n, f[22], inv[22];
inline long long read() {
  long long s = 0, f = 1;
  char c = getchar();
  while (c < '0' || c > '9') {
    if (c == '-') {
      f = -1;
    }
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    s = (s << 1) + (s << 3) + c - '0';
    c = getchar();
  }
  return s * f;
}
inline void write(long long x) {
  if (x < 0) {
    x = ~(x - 1);
    putchar('-');
  }
  if (x > 9) {
    write(x / 10);
  }
  putchar(x % 10 + '0');
}
long long power(long long a, long long p) {
  long long res = 1;
  while (p) {
    if (p & 1) res *= a, res %= mod;
    p >>= 1;
    a *= a;
    a %= mod;
  }
  return res;
}
long long c(long long n, long long m) {
  if (n < m || n < 0 || m < 0) {
    return 0;
  }
  n %= mod;
  if (n == 0 || m == 0) {
    return 1;
  }
  long long res = 1;
  for (long long i = 0; i < m; i++) {
    res *= n - i, res %= mod;
  }
  for (long long i = 1; i <= m; i++) {
    res *= inv[i], res %= mod;
  }
  return res;
}
signed main() {
  n = read(), m = read();
  for (long long i = 1; i <= n; i++) {
    f[i] = read();
  }
  for (long long i = 1; i <= 20; i++) {
    inv[i] = power(i, mod - 2);
  }
  long long ans = 0;
  for (long long i = 1; i < (1 << n); i++) {
    long long t = n + m - 1, bit = 0;
    for (long long j = 0; j < n; j++) {
      if (i & (1 << j)) {
        t -= f[j + 1] + 1;
        bit++;
      }
    }
    if (bit % 2 == 1) {
      ans = (ans + c(t, n - 1)) % mod;
    } else {
      ans = (ans - c(t, n - 1)) % mod;
    }
  }
  cout << (c(n + m - 1, n - 1) - ans + mod) % mod << endl;
  return 0;
}
