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 rep(i, n) for (int i = 0; i < (int)(n); i++)
#define ll long long
const ll p=1000000007;
int main(){
  int n,kk;
  cin >> n >> kk;
  string s;
  cin >> s;
  int ans=0;
  int r=0,l=0;
  int k[n];
  rep(i,n)k[i]=0;
  rep(i,n-1){
    if(s[i]=='1'&&s[i+1]=='0')k[i]=1;
    else if(s[i]!=s[i+1])k[i]=-1;
  }
  int cnt=0;
  if(s[0]=='0')cnt++;
  rep(i,n){
    while(r<n-1){
      if(cnt==kk&&k[r]==1)break;
      if(k[r]==1)cnt++;
      r++;
    }
    ans=max(ans,r-l+1);
    if(k[l]==-1)cnt--;
    l++;
  }
  cout << ans << endl;
}
