#include <bits/stdc++.h>
using namespace std;
template <typename kdl>
inline void read(kdl &x) {
  x = 0;
  int f = 1;
  char c = getchar();
  for (; c < '0' || '9' < c; c = getchar())
    if (c == '-') f = -1;
  for (; '0' <= c && c <= '9'; c = getchar())
    x = (x << 1) + (x << 3) + (c ^ 48);
  x *= f;
  return;
}
template <typename kdl>
inline void print(kdl x) {
  if (x < 0) putchar('-'), x = -x;
  if (x > 9) print(x / 10);
  putchar(x % 10 + 48);
  return;
}
const long long mod = 1000000007;
const long long maxn = 24;
long long mul(long long a, long long b) { return (a % mod) * (b % mod) % mod; }
long long Pow(long long a, long long b) {
  a %= mod;
  long long Ans = 1;
  while (b) {
    if (b & 1) Ans = mul(Ans, a);
    a = mul(a, a);
    b >>= 1;
  }
  return Ans;
}
long long jc(long long k) {
  long long Ans = 1;
  for (register long long i = 2; i <= k; i++) Ans *= i;
  return Ans;
}
long long n, lit;
long long s, ans;
long long f[maxn], inv[maxn];
long long C(long long a, long long b) {
  if (a < 0 || b < 0 || a > b) return 0;
  if (a == b) return 1;
  if (a == 0 || b == 0) return 1;
  b %= mod;
  long long Ans = inv[a];
  long long l = b - a + 1, r = b;
  for (register long long i = l; i <= r; i++) Ans = mul(Ans, i);
  return Ans;
}
int main() {
  read(n), read(s);
  inv[n] = Pow(jc(n), mod - 2);
  for (register long long i = n - 1; i >= 0; i--)
    inv[i] = mul(inv[i + 1], i + 1);
  lit = 1 << n;
  for (register long long i = 1; i <= n; i++) read(f[i]);
  ans = C(n - 1, n + s - 1);
  for (register long long i = 1; i < lit; i++) {
    long long w = n + s;
    long long cnt = 0, tot = 1;
    long long k = i;
    while (k) {
      if (k & 1) w -= f[tot], cnt++;
      tot++;
      k >>= 1;
    }
    w -= cnt + 1;
    if (cnt & 1)
      ans = (ans - C(n - 1, w)) % mod;
    else
      ans = (ans + C(n - 1, w)) % mod;
  }
  print((ans + mod) % mod), puts("");
  return 0;
}
