#include <bits/stdc++.h>
using namespace std;
const long long mod = 1000000007;
const long long INF = mod * mod;
const long double eps = 1e-8;
long long mod_pow(long long x, long long n) {
  long long ret = 1;
  while (n > 0) {
    if (n % 2) ret = ret * x % mod;
    x = x * x % mod;
    n >>= 1;
  }
  return ret;
}
struct perm {
 private:
  int sz;
  vector<long long> p, invp;

 public:
  perm(int n) {
    sz = n + 1;
    p.resize(sz), invp.resize(sz);
    p[0] = 1;
    for (int i = 1; i <= sz - 1; i++) {
      p[i] = p[i - 1] * i % mod;
    }
    invp[sz - 1] = 1;
    long long cop = mod - 2, x = p[sz - 1];
    while (cop) {
      if (cop % 2) invp[sz - 1] = invp[sz - 1] * x % mod;
      cop >>= 1;
      x = x * x % mod;
    }
    for (int i = sz - 1 - 1; i >= 0; i--) {
      invp[i] = invp[i + 1] * (i + 1) % mod;
    }
  }
  long long comb(long long x, long long y) {
    if (x < y || y < 0) return 0;
    long long ret = p[x];
    (ret *= invp[y]) %= mod;
    (ret *= invp[x - y]) %= mod;
    return ret;
  }
  long long combP(long long x, long long y) {
    if (x < y || y < 0) return 0;
    return p[x] * invp[x - y] % mod;
  }
};
perm p(1 << 19);
void solve() {
  int n;
  long long t;
  cin >> n >> t;
  vector<long long> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  a.push_back(INF);
  n++;
  vector<long long> ra(n + 1);
  for (int i = 0; i < n; i++) ra[i + 1] = ra[i] + a[i];
  long long ans = 0;
  for (int i = 1; i < n; i++) {
    long long ri = t - ra[i];
    if (ri > i) ri = i;
    long long le = t - ra[i] - (a[i] - 1);
    if (le < 0) le = 0;
    long long csum = 0;
    for (long long j = le; j <= ri; j++) {
      csum += p.comb(i, j);
      if (csum >= mod) csum -= mod;
    }
    long long b = mod_pow(2, i);
    b = mod_pow(b, mod - 2);
    csum = csum * b % mod;
    ans += csum * i % mod;
    if (ans >= mod) ans -= mod;
    long long dif = t - ra[i + 1];
    if (0 <= dif && dif <= i) {
      long long ad = p.comb(i, dif) * b % mod * (1 + mod) / 2 % mod;
      ans += ad * i % mod;
      if (ans >= mod) ans -= mod;
    }
  }
  cout << ans << endl;
}
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  solve();
  return 0;
}
