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;
using ll = long long;

ll memo[100000];

int main() {
  int N, K;
  string S;
  cin >> N >> K;
  cin >> S;
  int i=0,j=0;
  int ret = 0;
  while(j<N){
    while(j<N&&S[j]=='1')
      j++;
    ret = max(ret, j-i);
    while(j<N&&S[j]=='0')
      j++;
    K--;
    if(K<0){
      while(i<N&&S[i]=='1')
        i++;
      while(i<N&&S[i]=='0')
        i++;
      K++;
    }
    ret = max(ret, j-i);
  }
  cout << ret << endl;
}
