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: Runtime Error)

import java.util.*;

public class Main {
    public static void main(String[] args) throws Exception {
        // Your code here!
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        String s = sc.next();
        
        int[] sArray = new int[n + 1];
        int j = 0;
        int nowNum = 0;
        int count = 0;
        
        for (int i = 0; i < n; i++) {
            int num = Integer.valueOf(String.valueOf(s.charAt(i)));
            if (num == nowNum) {
                count++;
                continue;
            } else {
                sArray[j] = count;
                j++;
                count = 1;
                if (nowNum == 0) {
                    nowNum = 1;
                } else {
                    nowNum = 0;
                }
            }
        }
        sArray[j] = count;
        
        int max = 0;
        boolean end = false;
        for (int i = 0; i < n; i++) {
            int cnt = 0;
            if (i % 2 == 0) {
                for (int l = i; l < i + k * 2; l++) {
                    cnt += sArray[l];
                    if (l > j) end = true;
                }
                
            } else {
                for (int l = i; l <= i + k * 2; l++) {
                    cnt += sArray[l];
                    if (l > j) end = true;
                }
            }
            max = Math.max(max, cnt);
            if (end) break;
        }
        
        System.out.println(max);
    }
}