Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

5 1
00010

Sample Output 1

4

We can have four consecutive people standing on hands, which is the maximum result, by giving the following direction:

Give the direction with l = 1, r = 3, which flips the first, second and third persons from the left.

Sample Input 2

14 2
11101010110011

Sample Output 2

8

Sample Input 3

1 1
1

Sample Output 3

1

No directions are necessary.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
import java.io.*;

public class Main {

    private static int solver(String str, int k){
        int start = 0;
        int end=0;
        int order = 0;
        char stat = '1';

        int dist = 0;
        // ----
        while(order<=k && end<str.length()){
            if(str.charAt(end)!=stat){
                order++;
                stat = str.charAt(end);
                while(end<str.length() && str.charAt(end)==stat){
                    end++;
                }
            }else{
                end++;
            }
        }
        dist = Math.max(dist, end - start);

        while(end<str.length()) {
            char startStat = str.charAt(start);
            while (start < str.length() && str.charAt(start) == startStat) {
                start++;
            }
            end++;
            for(int i= end; i<str.length(); i++){
                if(str.charAt(i)=='0'){
                    end++;
                }
            }
            dist = Math.max(dist, end - start);

        }

        return dist;

    }

    public static void main(String[] args) {
        Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int n = in.nextInt();
        int k = in.nextInt();
        System.out.println(solver(in.next(), k));
    }
}