#include <bits/stdc++.h>
using namespace std;
template <typename T>
void read(T &x) {
  x = 0;
  char ch = getchar();
  long long f = 1;
  while (!isdigit(ch)) {
    if (ch == '-') f *= -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + ch - 48;
    ch = getchar();
  }
  x *= f;
}
int mod = 1000000007;
inline int mul(int x, int y) { return 1ll * x * y % mod; }
int add(int x, int y) { return x + y >= mod ? x + y - mod : x + y; }
int sub(int x, int y) { return x - y < 0 ? x - y + mod : x - y; }
int sq(int x) { return 1ll * x * x % mod; }
int pow(int a, int b) {
  return b == 0 ? 1 : (b & 1 ? mul(a, sq(pow(a, b / 2))) : sq(pow(a, b / 2)));
}
int n, t[1000020], fac[1000020], invfac[1000020];
int C(int n, int m) { return mul(fac[n], mul(invfac[n - m], invfac[m])); }
int cv = 1;
long long T, lwb = 0, upb = 0, mb = 0;
int main() {
  read(n);
  read(T);
  fac[0] = 1;
  for (int i = 1; i <= 1000010; i++) fac[i] = mul(i, fac[i - 1]);
  invfac[1000010] = pow(fac[1000010], mod - 2);
  for (int i = 1000010 - 1; i >= 0; i--) invfac[i] = mul(i + 1, invfac[i + 1]);
  int inv2 = (mod + 1) / 2, accu = 1, ans = 0;
  for (int i = 0; i < n; i++) {
    read(t[i]);
    lwb += t[i];
    upb += t[i] + 1;
    mb += t[i];
    if (lwb > T) break;
    cv = sub(mul(cv, 2), C(upb - lwb - 1, mb - lwb));
    while (mb < T && mb < upb) {
      cv = add(cv, C(upb - lwb, mb - lwb + 1));
      mb += 1;
    }
    while (mb > T) {
      cv = sub(cv, C(upb - lwb, mb - lwb));
      mb -= 1;
    }
    accu = mul(accu, inv2);
    ans = add(ans, mul(cv, accu));
  }
  cout << ans << endl;
  return 0;
}
