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: Accepted)


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

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		sc.nextInt();
		int k = sc.nextInt();
		sc.nextLine();
		String s = sc.nextLine();
		Column c = new Column(s);
		int h = c.getHandsSize();
		if(k >= h) {
			k = h - 1;
		}
		int maxPoint = 0;
		for(int i = 0; i < h - k; i++) {
			int point = c.getPoint(i, i + k);
//			System.out.println(point);
			if(point > maxPoint) {
				maxPoint = point;
			}
		}
		System.out.println(maxPoint);
	}

}
class Column{
	ArrayList<Integer> Hands = new ArrayList<Integer>();
	ArrayList<Integer> Stands = new ArrayList<Integer>();
	Column(String s){
		StringBuilder sb = new StringBuilder(s);
		while(sb.length() != 0){
			addHandStand(sb);
		}
		if(Stands.get(Stands.size() - 1) != 0) {
			Hands.add(0);
		}
	}
	void addHandStand(StringBuilder sb) {
		int h = sb.indexOf("0");
		if(h == -1) {
			h = sb.length();
		}
		Hands.add(h);
		sb.delete(0, h);

		int s = sb.indexOf("1");
		if(s == -1) {
			s = sb.length();
		}
		Stands.add(s);
		sb.delete(0, s);
	}
	int getPoint(int i, int i2) {
		if(i2 > Hands.size() - 1) {
			i2 = Hands.size() -1;
		}
		if(i == i2) {
			return Hands.get(i);
		}else if(i > i2){
			return 0;
		}
		int point =Hands.get(i2);
		for(; i < i2; i++) {
			point += Hands.get(i) + Stands.get(i);
		}
		return point;
	}
	int getHandsSize() {
		return Hands.size();
	}
}