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 <iostream>
#include <string>
#include <algorithm>
using namespace std;
int N, K; string S;
int main() {
  cin >> N >> K >> S;
  int t[100005];
  if(S[0] == '0') t[0] = 1;
  for(int i = 0; i < N; ++i) {
    if(S[i] == '1' && S[i+1] == '0') t[i+1] = t[i]+1;
    else t[i+1] = t[i];
  }
  int ans = 0;
  for(int i = 0; i < N; ++i) {
    int l = i, r = N;
    while(r-l > 1) {
      int m = (l+r)/2;
      int diff = t[m]-t[i];
      if(S[i] == '0') ++diff;
      if(diff > K) r = m;
      else l = m;
    }
    ans = max(ans, l-i+1);
  }
  cout << ans << endl;
}