#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 1, mod = 1e9 + 7;
inline long long binpow(long long a, long long s) {
  long long ans = 1;
  while (s) {
    if (s & 1) ans = ans * a % mod;
    a = a * a % mod;
    s >>= 1;
  }
  return ans;
}
inline long long inv(long long a) { return binpow(a, mod - 2); }
int n;
long long t;
long long a[N];
long long sum[N];
long long ans;
long long fact[N], inv_fact[N], pow2[N], inv_pow2[N];
void init() {
  long long inv_2 = inv(2);
  fact[0] = 1;
  inv_fact[0] = 1;
  pow2[0] = 1;
  inv_pow2[0] = 1;
  for (int i = 1; i < N; ++i) {
    fact[i] = fact[i - 1] * i % mod;
    inv_fact[i] = inv(fact[i]);
    pow2[i] = pow2[i - 1] * 2 % mod;
    inv_pow2[i] = inv_pow2[i - 1] * inv_2 % mod;
  }
}
long long C(long long n, long long k) {
  if (n < k) return 0ll;
  return fact[n] * inv_fact[k] % mod * inv_fact[n - k] % mod;
}
int main() {
  ios_base::sync_with_stdio(false);
  cout.tie(0);
  cin.tie(0);
  init();
  cin >> n >> t;
  for (int i = 0; i < n; ++i) cin >> a[i];
  if (a[0] > t) {
    cout << "0\n";
    return 0;
  }
  sum[0] = a[0];
  for (int i = 1; i < n; ++i) sum[i] = sum[i - 1] + a[i];
  long long x = (a[0] + 1 > t ? 0 : 1), p = 1 + x;
  ans = (x ? 1 : inv_pow2[1]);
  for (int i = 1; i < n; ++i) {
    p = (p * 2 + C(i, ++x)) % mod;
    while (x >= 0 && sum[i] + x > t) p = (p + mod - C(i + 1, x--)) % mod;
    ans = (ans + p * inv_pow2[i + 1]) % mod;
  }
  cout << ans << '\n';
}
