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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;

public class Main {
	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		String[] nk = in.readLine().split(" ");
		String s = in.readLine();
		int op = Integer.valueOf(nk[1]);
		int mostlong = 0;
		
		
		
		StringBuilder sb = new StringBuilder(s);
		ArrayList<Short> list = new ArrayList<>();
		
		if(s.startsWith("0")) {
			list.add((short) 0);
		}
		short temp = 0;
		char now = sb.charAt(0);
		for(int i = 0; i < sb.length(); i++) {
			if(now == sb.charAt(i)) {
				temp ++;
			}else {
				now = sb.charAt(i);
				list.add(temp);
				temp = 1;
			}
		}
		list.add(temp);
		int cache = 0;
		for(int i = 0; i < ((list.size() / 2) + 1) - 2; i++) {
			cache = 0;
			for(int j = 0; j < (op * 2) + 1; j++) {
				cache += list.get(i*2 + j);
				if(cache > mostlong) {
					mostlong = cache;
				}
			}
		}
		if(list.size() == 1) {
			int te = list.get(0);
			System.out.println(te);
		}else {
			System.out.println(mostlong);
		}
	}
}