#include <bits/stdc++.h>
using namespace std;
const long long mod = (long long)1e9 + 7;
long long binpow(long long a, long long n) {
  if (n == 0) return 1;
  if (n % 2 == 1)
    return (binpow(a, n - 1) * a) % mod;
  else {
    long long b = binpow(a, n / 2);
    return (b * b) % mod;
  }
}
long long add(long long x, long long y) { return (x + y) % mod; }
long long sub(long long x, long long y) {
  x -= y;
  if (x < 0) x += mod;
  return x;
}
long long mult(long long x, long long y) { return (x * y) % mod; }
long long rev(long long x) { return binpow(x, mod - 2); }
int n;
long long T;
long long t[400400], second[400400], fact[400400], rev_fact[400400], m[400400],
    pw2[400400], rev_pw2[400400];
long long cnk(long long n, long long k) {
  long long result = mult(fact[n], mult(rev_fact[n - k], rev_fact[k]));
  return result;
}
int main() {
  ios_base ::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> T;
  fact[0] = 1;
  rev_fact[0] = 1;
  pw2[0] = 1;
  rev_pw2[0] = 1;
  for (int i = 1; i <= n; ++i) {
    cin >> t[i];
    second[i] = second[i - 1] + t[i];
    fact[i] = mult(i, fact[i - 1]);
    rev_fact[i] = rev(fact[i]);
    pw2[i] = mult(2, pw2[i - 1]);
    rev_pw2[i] = rev(pw2[i]);
  }
  long long sum = 0, ans = 0;
  long long rev2 = rev(2);
  for (int i = 1; i <= n; ++i) {
    m[i] = min((long long)i, T - second[i]);
    if (m[i] < 0) break;
    if (i > 1) {
      sum = mult(sum, 2);
      sum = add(sum, cnk(i, m[i - 1] + 1));
      sum = sub(sum, cnk(i - 1, 0));
      sum = add(sum, cnk(i, 0));
      sum = sub(sum, cnk(i - 1, m[i - 1]));
    } else {
      sum = cnk(1, 0) + cnk(1, 1);
    }
    long long ind = m[i - 1] + 1;
    while (ind > m[i]) {
      sum = sub(sum, cnk(i, ind));
      --ind;
    }
    ans = add(ans, mult(sum, rev_pw2[i]));
  }
  cout << ans << "\n";
  return 0;
}
