#include <bits/stdc++.h>
using namespace std;
const long long INF = 2e18;
const int INFi = 2e9;
const int maxN = 2e5 + 5;
const int P = 998244353;
const int md = 1e9 + 7;
double getTime() { return clock() / (double)CLOCKS_PER_SEC; };
int mul(int a, int b) { return (1ll * a * b) % md; }
int add(int a, int b) {
  if (a + b >= md) return a + b - md;
  return a + b;
}
int sub(int a, int b) {
  if (a - b < 0) return a - b + md;
  return a - b;
}
int binpow(int a, int b) {
  if (b == 0) return 1;
  if (b % 2) return mul(a, binpow(a, b - 1));
  int mid = binpow(a, b / 2);
  return mul(mid, mid);
}
int rev(int a) { return binpow(a, md - 2); }
int fact[maxN];
int C(int n, int k) {
  return mul(fact[n], mul(rev(fact[k]), rev(fact[n - k])));
}
void solve() {
  fact[0] = 1;
  for (int i = 1; i < maxN; ++i) fact[i] = mul(fact[i - 1], i);
  int n;
  long long T;
  cin >> n >> T;
  vector<long long> t(n);
  for (int i = 0; (i) < n; ++(i)) cin >> t[i];
  for (int i = 1; i < n; ++i) t[i] += t[i - 1];
  int p = 0;
  int j = 0;
  for (int i = n - 1; i >= 0; --i) {
    int c = i + 1;
    j = max(0, min(j, c));
    long long time = t[i] + j;
    while (time <= T && j <= c) {
      if (c == n || t[c] + j > T) {
        int k = mul(C(c, j), binpow(2, n - c));
        p = add(p, mul(c, k));
      } else if (t[c] + j + 1 > T) {
        int k = mul(C(c, j), binpow(2, n - c - 1));
        p = add(p, mul(c, k));
      }
      j++;
      time++;
    }
    j--;
  }
  cout << mul(p, rev(binpow(2, n)));
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  int tests = 1;
  for (int _ = 0; (_) < tests; ++(_)) {
    solve();
  }
  return 0;
}
