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> list = new ArrayList<>();
        //11101010110011
        int begin = 0;
        char now = '1';

        for (int i = 0; i < n; i++) {
            if (s.charAt(i) != now) {
                list.add(i - begin);
                now = s.charAt(i);
                begin = i;
            }
        }
        list.add(n - begin);
        if (now == '0') list.add(0);

        int result = 0, sum = 0, left = 0, right = 0;
        for (int i = 0; i < list.size(); i += 2) {
            int nextLeft = i;
            int nextRight = Math.min(i + k * 2 + 1, list.size());

            while (nextLeft > left) {
                sum -= list.get(left);
                left++;
            }

            while (nextRight > right) {
                sum += list.get(right);
                right++;
            }
            result = Math.max(sum, result);
        }

        System.out.println(result);
    }

}