#include <bits/stdc++.h>
using namespace std;
const long long N = 200001;
long long a[N];
long long b[N];
long long c[N];
int main() {
  long long n, k;
  cin >> n >> k;
  for (long long i = 0; i <= n; i++) {
    cin >> a[i];
  }
  b[n] = a[n];
  long long right = 0;
  for (long long i = n - 1; i >= 0; i--) {
    b[i] = a[i] + 2 * b[i + 1];
    if (b[i] > n * k || b[i] < -n * k) {
      right = i;
      break;
    }
  }
  long long left = n;
  long long cur_val = a[0];
  c[0] = a[0];
  for (long long i = 1; i <= n; i++) {
    if (cur_val % 2 != 0) {
      left = i - 1;
      break;
    } else {
      cur_val /= 2;
      cur_val += a[i];
      c[i] = cur_val;
    }
  }
  long long ans = 0;
  for (long long i = right; i <= left; i++) {
    long long x = c[i] + b[i] - 2 * a[i];
    if (i == n) {
      if (x != 0) {
        ans++;
      }
    } else {
      if (abs(x) <= k) {
        ans++;
      }
    }
  }
  cout << ans << endl;
}

### Prompt

Please formulate a Cpp solution to the following problem:

Limak is a little polar bear. He doesn't have many toys and thus he often plays with polynomials.

He considers a polynomial valid if its degree is n and its coefficients are integers not exceeding k by the absolute value. More formally:

Let a0, a1, ..., an denote the coefficients, so <image>. Then, a polynomial P(x) is valid if all the following conditions are satisfied:

  * ai is integer for every i; 
  * |ai| ≤ k for every i; 
  * an ≠ 0. 



Limak has recently got a valid polynomial P with coefficients a0, a1, a2, ..., an. He noticed that P(2) ≠ 0 and he wants to change it. He is going to change one coefficient to get a valid polynomial Q of degree n that Q(2) = 0. Count the number of ways to do so. You should count two ways as a distinct if coefficients of target polynoms differ.

Input

The first line contains two integers n and k (1 ≤ n ≤ 200 000, 1 ≤ k ≤ 109) — the degree of the polynomial and the limit for absolute values of coefficients.

The second line contains n + 1 integers a0, a1, ..., an (|ai| ≤ k, an ≠ 0) — describing a valid polynomial <image>. It's guaranteed that P(2) ≠ 0.

Output

Print the number of ways to change one coefficient to get a valid polynomial Q that Q(2) = 0.

Examples

Input

3 1000000000
10 -9 -3 5


Output

3


Input

3 12
10 -9 -3 5


Output

2


Input

2 20
14 -7 19


Output

0

Note

In the first sample, we are given a polynomial P(x) = 10 - 9x - 3x2 + 5x3.

Limak can change one coefficient in three ways:

  1. He can set a0 = - 10. Then he would get Q(x) = - 10 - 9x - 3x2 + 5x3 and indeed Q(2) = - 10 - 18 - 12 + 40 = 0. 
  2. Or he can set a2 = - 8. Then Q(x) = 10 - 9x - 8x2 + 5x3 and indeed Q(2) = 10 - 18 - 32 + 40 = 0. 
  3. Or he can set a1 = - 19. Then Q(x) = 10 - 19x - 3x2 + 5x3 and indeed Q(2) = 10 - 38 - 12 + 40 = 0. 



In the second sample, we are given the same polynomial. This time though, k is equal to 12 instead of 109. Two first of ways listed above are still valid but in the third way we would get |a1| > k what is not allowed. Thus, the answer is 2 this time.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const long long N = 200001;
long long a[N];
long long b[N];
long long c[N];
int main() {
  long long n, k;
  cin >> n >> k;
  for (long long i = 0; i <= n; i++) {
    cin >> a[i];
  }
  b[n] = a[n];
  long long right = 0;
  for (long long i = n - 1; i >= 0; i--) {
    b[i] = a[i] + 2 * b[i + 1];
    if (b[i] > n * k || b[i] < -n * k) {
      right = i;
      break;
    }
  }
  long long left = n;
  long long cur_val = a[0];
  c[0] = a[0];
  for (long long i = 1; i <= n; i++) {
    if (cur_val % 2 != 0) {
      left = i - 1;
      break;
    } else {
      cur_val /= 2;
      cur_val += a[i];
      c[i] = cur_val;
    }
  }
  long long ans = 0;
  for (long long i = right; i <= left; i++) {
    long long x = c[i] + b[i] - 2 * a[i];
    if (i == n) {
      if (x != 0) {
        ans++;
      }
    } else {
      if (abs(x) <= k) {
        ans++;
      }
    }
  }
  cout << ans << endl;
}

```