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 {

	/**
	 * 
	 * @param args
	 */
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int N = scan.nextInt();
		int K = scan.nextInt();
		String S = scan.next();
		
		scan.close();
		
		int saka = Integer.parseInt(String.valueOf(S.charAt(0)));
		int c = 0;
		List<Integer> list = new ArrayList<>();
		List<Integer> list2 = new ArrayList<>();
		for(int i=0; i<N; i++) {
			if(saka == Integer.parseInt(String.valueOf(S.charAt(i)))) {
				c++;
			} else {
				list.add(c);
				list2.add(saka);
				saka = Integer.parseInt(String.valueOf(S.charAt(i)));
				c=1;
			}
		}
		list.add(c);
		list2.add(saka);
		//System.out.println(list.toString());
		//System.out.println(list2.toString());
		
		int r = 0;
		for(int h=0; h<list.size(); h++) {
			int sakaCount = 0;
			int changeCount = 0;
			for(int i=h; i<list.size(); i++) {
				if(list2.get(i) == 0) {
					changeCount++;
					if(changeCount>K) {
						if(r<sakaCount) {
							r = sakaCount;
						}
						//System.out.println(sakaCount);
						sakaCount = 0;
						changeCount = 0;
						break;
					} else {
						sakaCount+=list.get(i);
						
					}
				} else {
					sakaCount+=list.get(i);

				}

			}
			if(r<sakaCount) {
				r = sakaCount;
			}
		}

		System.out.println(r);


	
	}

}