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: Time Limit Exceeded)

import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {

	static int ans;

	public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        String s = sc.next();
        solve(n, k, s);
    }

    static void solve(int n, int k, String s) {
    	List<Integer> list = new ArrayList<>();
    	method(list, s);

    	ans = 0;
    	for(int i = 0; i < list.size(); i++) {
    		int tmp = sum(list,i,k);
    		ans = Math.max(ans, tmp);
    	}
    	System.out.println(ans);
    }

    static int sum(List<Integer> list, int index, int num) {
    	int sum = 0;
    	int count = 0;
    	boolean boo = true;
    	while(index < list.size()) {
    		int tmp = list.get(index);
    		if(tmp < 0) {
    			count++;
    		}
    		if(count > num) {
    			boo = false;
    			break;
    		}
    		sum += Math.abs(tmp);
    		index++;
    	}
    	if(boo) {
    		System.out.println(Math.max(sum, ans));
    		System.exit(0);
    	}
    	return sum;
    }

    static void method(List<Integer> list, String s) {
    	int i = 0;
    	while(i < s.length()) {
    		int count = 0;
    		int j = i;
    		while(j < s.length() && s.charAt(i) == s.charAt(j)) {
    			count++;
    			j++;
    		}
    		if(s.charAt(i) == '1') {
    			list.add(count);
    		} else {
    			list.add(count * -1);
    		}
    		i = j;
    	}
    }
}