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;
int main()
{
  int n,k,i;
  cin>>n>>k;
  string s;
  cin>>s;
  int res=1;
  int l=0,r=1;
  int t=(s[0]=='1')?0:1;
  while(r<n)
  {
    if(s[r-1]=='1' && s[r]=='0')
    {
   		t++;
      	if(t>k)
        {
          while(1)
          {
            l++;
            if(s[l-1]=='0' && s[l]=='1') break;
          }
          t--;
        } 
    }
    res=max(res,r-l+1);
    r++;
  }
  cout<<res;
  return 0;	
}
