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;
#define ll long long
typedef pair<ll,ll> P;
#define M 1000000007
int main(){
  ll n,k,c=0,cnt=0,f=0,b=0;
  string s;
  cin>>n>>k>>s;
  if(n==1){cout<<1;return 0;}
  if(s[0]=='0') cnt++;
  for(int i=1;i<n;i++){
    if(s[i]!=s[i-1]){
      if(s[i]=='1') ;
      else{
        if(cnt<k){
          cnt++;
        }else{
          while(true){
            b++;
            if(s[b]=='1'&&s[b-1]=='0'){
              break;
            }
          }
        }
      }
    }
    c=max(c,i-b+1);
  }
  cout<<c;
}
