#include <bits/stdc++.h>
#pragma GCC optimize("Ofast", "unroll-loops")
using namespace std;
const int maxn = 2e5 + 5;
const int iinf = 1 << 29;
const long long inf = 1ll << 60;
const long long mod = 1e9 + 7;
void GG() {
  cout << "No\n";
  exit(0);
}
long long mpow(long long a, long long n) {
  long long re = 1;
  while (n > 0) {
    if (n & 1) re = re * a % mod;
    a = a * a % mod;
    n >>= 1;
  }
  return re;
}
long long inv(long long b) {
  if (b == 1) return b;
  return (mod - mod / b) * inv(mod % b) % mod;
}
long long fac[maxn];
void build() {
  fac[0] = 1;
  for (int i = (1); i < (maxn); i++) {
    fac[i] = fac[i - 1] * i % mod;
  }
}
long long C(long long a, long long b) {
  return fac[a] * inv(fac[a - b]) % mod * inv(fac[b]) % mod;
}
int main() {
  ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  build();
  int n;
  long long t;
  cin >> n >> t;
  vector<long long> a(n);
  for (int i = 0; i < (n); i++) cin >> a[i];
  long long nx = 0;
  long long p2 = 1;
  long long x = 0;
  long long re = 0;
  long long sum = 0;
  for (int i = 0; i < (n); i++) {
    p2 = p2 * 2 % mod;
    sum += a[i];
    if (sum > t) break;
    if (sum + i + 1 > t) {
      if (nx == 0)
        nx = p2, x = i + 2;
      else {
        nx = (mod + nx * 2 - C(i, x - 1)) % mod;
      }
      while (sum + x > 1 + t) {
        nx = (mod + nx - C(i + 1, x - 1)) % mod;
        x--;
      }
      re += nx * inv(p2) % mod;
      re %= mod;
    } else {
      re++;
      re %= mod;
    }
  }
  cout << re << '\n';
}
