#include <bits/stdc++.h>
using namespace std;
int n;
long long k;
int cnt[212345], a[212345], v[212345];
int main() {
  memset(cnt, 0, sizeof(cnt));
  memset(a, 0, sizeof(a));
  memset(v, 0, sizeof(v));
  ios::sync_with_stdio(0);
  cin >> n >> k;
  for (int i = 0; i <= n; i++) {
    cin >> a[i];
    int x = a[i];
    int j = 0;
    while (x) {
      cnt[i + j] += x % 2;
      x /= 2;
      j++;
    }
  }
  int j = 0, t, f = 1;
  for (int i = 0; i <= n + 100; i++) {
    t = j + cnt[i];
    cnt[i] = t % 2;
    j = t / 2;
    if (cnt[i] < 0)
      f = -1;
    else if (cnt[i] > 0)
      f = 1;
  }
  if (f < 0)
    for (int i = 0; i <= n + 100; i++) cnt[i] *= -1;
  int fl = 0;
  for (int i = 0; i <= n + 100; i++) {
    if (fl) {
      if (cnt[i] == 1) fl = 0;
      cnt[i] = (cnt[i] + 1) % 2;
    } else {
      if (cnt[i] == -1) {
        cnt[i] = 1;
        fl = 1;
      }
    }
  }
  for (int i = 0; i <= n; i++) {
    v[i] = 1;
    if (cnt[i]) break;
  }
  int ans = 0;
  long long tp = 0;
  f *= -1;
  for (int i = n + 100; i >= 0; i--) {
    tp = tp * 2 + cnt[i] * f;
    if (abs(tp + a[i]) <= k && v[i]) {
      if (i == n && abs(tp + a[i]) == 0) continue;
      ans++;
    }
    if (abs(tp) > 2 * k) break;
  }
  cout << ans << endl;
}

### Prompt

In cpp, your task is to solve 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;
int n;
long long k;
int cnt[212345], a[212345], v[212345];
int main() {
  memset(cnt, 0, sizeof(cnt));
  memset(a, 0, sizeof(a));
  memset(v, 0, sizeof(v));
  ios::sync_with_stdio(0);
  cin >> n >> k;
  for (int i = 0; i <= n; i++) {
    cin >> a[i];
    int x = a[i];
    int j = 0;
    while (x) {
      cnt[i + j] += x % 2;
      x /= 2;
      j++;
    }
  }
  int j = 0, t, f = 1;
  for (int i = 0; i <= n + 100; i++) {
    t = j + cnt[i];
    cnt[i] = t % 2;
    j = t / 2;
    if (cnt[i] < 0)
      f = -1;
    else if (cnt[i] > 0)
      f = 1;
  }
  if (f < 0)
    for (int i = 0; i <= n + 100; i++) cnt[i] *= -1;
  int fl = 0;
  for (int i = 0; i <= n + 100; i++) {
    if (fl) {
      if (cnt[i] == 1) fl = 0;
      cnt[i] = (cnt[i] + 1) % 2;
    } else {
      if (cnt[i] == -1) {
        cnt[i] = 1;
        fl = 1;
      }
    }
  }
  for (int i = 0; i <= n; i++) {
    v[i] = 1;
    if (cnt[i]) break;
  }
  int ans = 0;
  long long tp = 0;
  f *= -1;
  for (int i = n + 100; i >= 0; i--) {
    tp = tp * 2 + cnt[i] * f;
    if (abs(tp + a[i]) <= k && v[i]) {
      if (i == n && abs(tp + a[i]) == 0) continue;
      ans++;
    }
    if (abs(tp) > 2 * k) break;
  }
  cout << ans << endl;
}

```