#include <bits/stdc++.h>
using namespace std;
inline long long read() {
  char ch = getchar();
  long long nega = 1;
  while (!isdigit(ch)) {
    if (ch == '-') nega = -1;
    ch = getchar();
  }
  long long ans = 0;
  while (isdigit(ch)) {
    ans = ans * 10 + ch - 48;
    ch = getchar();
  }
  if (nega == -1) return -ans;
  return ans;
}
long long fac[200005];
long long inv[200005];
long long a[200005];
long long C(long long x, long long y) {
  return fac[x] * inv[y] % 1000000007 * inv[x - y] % 1000000007;
}
long long qpow(long long x, long long y) {
  long long ans = 1;
  while (y) {
    if (y & 1) ans = ans * x % 1000000007;
    x = x * x % 1000000007;
    y >>= 1;
  }
  return ans;
}
signed main() {
  long long n, T;
  cin >> n >> T;
  for (long long i = 1; i <= n; i++) {
    a[i] = read();
    a[i] += a[i - 1];
  }
  fac[0] = fac[1] = 1;
  inv[0] = inv[1] = 1;
  for (long long i = 2; i <= n; i++) {
    fac[i] = fac[i - 1] * i % 1000000007;
    inv[i] = (1000000007 - 1000000007 / i) * inv[1000000007 % i] % 1000000007;
  }
  for (long long i = 2; i <= n; i++) inv[i] = inv[i - 1] * inv[i] % 1000000007;
  long long ans = 0, tmp = 0;
  bool DO = true;
  long long siz = 0;
  for (long long i = 1; i <= n; i++) {
    if (T - a[i] >= i)
      ans = (ans + 1) % 1000000007;
    else {
      if (T - a[i] < 0) break;
      if (DO) {
        DO = false;
        siz = T - a[i];
        for (long long j = 0; j <= siz; j++) {
          tmp = (tmp + C(i, j)) % 1000000007;
        }
        ans = (ans + tmp * qpow(qpow(2, i), 1000000007 - 2) % 1000000007) %
              1000000007;
      } else {
        long long x = T - a[i];
        for (long long j = x + 1; j <= siz; j++) {
          tmp = (tmp - C(i - 1, j) + 1000000007) % 1000000007;
        }
        siz = x;
        tmp = tmp * 2 % 1000000007;
        tmp = (tmp - C(i - 1, x) + 1000000007) % 1000000007;
        ans = (ans + tmp * qpow(qpow(2, i), 1000000007 - 2) % 1000000007) %
              1000000007;
      }
    }
  }
  cout << ans << endl;
  return 0;
}
