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.LinkedList;
import java.util.Scanner;

public class Main {
    public static void main(String args[]) {
        try (Scanner in = new Scanner(System.in)) {
            int N = in.nextInt();
            int K = in.nextInt();
            String S = in.next();
            S += '-';
            char[] cs = S.toCharArray();

            int max = 0;
            int sum = 0;
            int size0 = 0;
            LinkedList<Integer> l = new LinkedList<>();
            for (int i = 0, count1 = 0, count0 = 0; i < cs.length; i++) {
                if (cs[i] == '0') {
                    count0++;
                    if (count1 > 0) {
                        l.add(count1);
                        sum += count1;
                        count1 = 0;
                        max = Math.max(max, sum);
//                        Utils.debug(i, max, sum);
                    }
                } else if (cs[i] == '1') {
                    count1++;
                    if (count0 > 0) {
                        l.add(count0);
                        size0++;
                        sum += count0;
                        count0 = 0;
                        if (size0 > K) {
                            if (l.size() % 2 == 0) {
                                int count12 = l.pollFirst();
                                sum -= count12;
                                int count02 = l.pollFirst();
                                sum -= count02;
                            } else {
                                int count02 = l.pollFirst();
                                sum -= count02;
                            }
                            size0--;
                        }
                        max = Math.max(max, sum);
//                        Utils.debug(i, max, sum);
                    }
                } else {
                    if (count1 > 0) {
                        l.add(count1);
                        sum += count1;
                        count1 = 0;
                        max = Math.max(max, sum);
//                        Utils.debug(i, max, sum);
                    }
                    if (count0 > 0) {
                        l.add(count0);
                        size0++;
                        sum += count0;
                        count0 = 0;
                        if (size0 > K) {
                            if (l.size() % 2 == 0) {
                                int count12 = l.pollFirst();
                                sum -= count12;
                                int count02 = l.pollFirst();
                                sum -= count02;
                            } else {
                                int count02 = l.pollFirst();
                                sum -= count02;
                            }
                            size0--;
                        }
                        max = Math.max(max, sum);
//                        Utils.debug(i, max, sum);
                    }
                }
            }

            System.out.println(max);

        }
    }
}
