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;
int main() {
    int n,k;
    cin>>n>>k;
    string s;
    cin>>s;
    int l=0,r=1;
    int tk=s[0]=='1'?0:1;
    int ts= 1;
int ms=ts;
    while(r<n){
        if(s[r-1]=='1'&&s[r]=='0')++tk;
        if(tk>k){
            while(l<r&&(s[l]!='0'||s[l+1]!='1')){
                ++l;
                --ts;
            }
            ++l;--ts;
            --tk;
        }
        ++ts;
        ++r;
        ms=max(ms,ts);
//cout<<ts<<" "<<tk<<endl;
    }
    cout<<ms<<endl;

    return 0;
}
