N people are arranged in a row from left to right.

You are given a string S of length N consisting of `0` and `1`, and a positive integer K.

The i-th person from the left is standing on feet if the i-th character of S is `0`, and standing on hands if that character is `1`.

You will give the following direction at most K times (possibly zero):

Direction: Choose integers l and r satisfying 1 \leq l \leq r \leq N, and flip the l-th, (l+1)-th, ..., and r-th persons. That is, for each i = l, l+1, ..., r, the i-th person from the left now stands on hands if he/she was standing on feet, and stands on feet if he/she was standing on hands.

Find the maximum possible number of consecutive people standing on hands after at most K directions.

Constraints

* N is an integer satisfying 1 \leq N \leq 10^5.
* K is an integer satisfying 1 \leq K \leq 10^5.
* The length of the string S is N.
* Each character of the string S is `0` or `1`.

Input

Input is given from Standard Input in the following format:


N K
S


Output

Print the maximum possible number of consecutive people standing on hands after at most K directions.

Examples

Input

5 1
00010


Output

4


Input

14 2
11101010110011


Output

8


Input

1 1
1


Output

1
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define mod 1000000007

int main() {
    int N, K;
  cin >> N >> K;
  string s;
  cin >> s;

  int ans = 0, r = 0, cont = 0;

  if (s[0] == '0') cont++;

  for (int l = 0; l < N; l++) {

    while (cont <= K && r < N) {
      if (r + 1 < N && s[r] == '1' && s[r + 1] == '0') cont++;
      r++;
    }

    ans = max(ans, r - l);

    if (l + 1 < N && s[l] == '0' && s[l + 1] == '1') cont--;
  }

  cout << ans << endl;
}