#include <bits/stdc++.h>
using namespace std;
const int MOD = 1000000007;
long long POW(long long a, long long b, long long MMM = MOD) {
  long long ret = 1;
  for (; b; b >>= 1, a = (a * a) % MMM)
    if (b & 1) ret = (ret * a) % MMM;
  return ret;
}
long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
long long lcm(long long a, long long b) {
  if (a == 0 || b == 0) return a + b;
  return a * (b / gcd(a, b));
}
int dx[] = {0, 1, 0, -1, 1, 1, -1, -1}, dy[] = {1, 0, -1, 0, 1, -1, 1, -1};
int ddx[] = {-1, -2, 1, -2, 2, -1, 2, 1}, ddy[] = {-2, -1, -2, 1, -1, 2, 1, 2};
long long fac[200001], inv[200001], t[200002], p[200002];
long long nCr(int n, int r) {
  if (r < 0 || r > n) return 0;
  long long c = fac[n];
  c = (c * inv[r]) % MOD;
  c = (c * inv[n - r]) % MOD;
  return c;
}
int main() {
  int n;
  long long T;
  scanf("%d%lld", &n, &T);
  fac[0] = inv[0] = 1;
  for (int(i) = (1); (i) <= (200000); (i) += (1))
    fac[i] = (fac[i - 1] * i) % MOD;
  inv[200000] = POW(fac[200000], MOD - 2);
  for (int(i) = (199999); (i) >= (1); (i) -= (1))
    inv[i] = (inv[i + 1] * (i + 1)) % MOD;
  p[0] = 1, p[1] = inv[2];
  for (int(i) = (2); (i) <= (200000); (i) += (1))
    p[i] = (p[i - 1] * p[1]) % MOD;
  long long ans = 0, S = 0;
  for (int(i) = (1); (i) <= (n); (i) += (1)) scanf("%lld", t + i);
  t[n + 1] = 987654321987654321;
  long long tmp = 0, l = 0, r = -1;
  for (int(x) = (1); (x) <= (n); (x) += (1)) {
    S += t[x];
    long long L = max(0LL, T - S - t[x + 1] + 1), R = min(1LL * x, T - S);
    if (L <= R) {
      while (r < R) tmp = (tmp + nCr(x, ++r)) % MOD;
      while (r > R) tmp = (tmp + MOD - nCr(x, r--)) % MOD;
      while (l > L) tmp = (tmp + nCr(x, --l)) % MOD;
      while (l < L) tmp = (tmp + MOD - nCr(x, l++)) % MOD;
      ans = (ans + (tmp * p[x]) % MOD * x) % MOD;
    }
    long long LL = max(0LL, T - S - t[x + 1]);
    if (LL <= R) {
      while (r < R) tmp = (tmp + nCr(x, ++r)) % MOD;
      while (r > R) tmp = (tmp + MOD - nCr(x, r--)) % MOD;
      while (l > LL) tmp = (tmp + nCr(x, --l)) % MOD;
      while (l < LL) tmp = (tmp + MOD - nCr(x, l++)) % MOD;
      ans = (ans + (tmp * p[x]) % MOD * x) % MOD;
    }
    tmp = (tmp + tmp + nCr(x, l - 1) - nCr(x, r)) % MOD;
  }
  ans = (ans * inv[2]) % MOD;
  printf("%lld", ans);
}
