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
import java.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        String s = sc.next();
        List<Integer> shiseiList = new ArrayList<>();

        for (int i = 0; i < s.length(); i++){
            int value = Character.getNumericValue(s.charAt(i));
            shiseiList.add(value);
        }

        List<Integer> changePointList = new ArrayList<>();

        for (int i = 0; i < n; i++){
            if (i == 0){
                changePointList.add(i);
            }else {
                if (!shiseiList.get(i).equals(shiseiList.get(i - 1))){
                    changePointList.add(i);
                }
            }
        }
        // end point
        changePointList.add(n);
        int changeSize = changePointList.size();
        List<Integer> answerList = new ArrayList<>();

        for (int i = 0; i < changeSize - 1; i++){
            int shisei = shiseiList.get(changePointList.get(i));
            if (shisei == 1){
                int endIndex = Math.min(i + k * 2 + 1, changeSize - 1);
                answerList.add(changePointList.get(endIndex) - changePointList.get(i));
            }else {
                int endIndex = Math.min(i + 2 * k, changeSize - 1);
                answerList.add(changePointList.get(endIndex) - changePointList.get(i));
            }
        }

        answerList.sort(Comparator.reverseOrder());

        System.out.println(answerList.get(0));

    }

}