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.io.*;
import java.util.ArrayList;

class Main{
    public static void main(String[] args) throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String str = br.readLine();
        String[] sl = str.split(" ");
        int N = Integer.parseInt(sl[0]);
        int K = Integer.parseInt(sl[1]);
        str = br.readLine();
        ArrayList<Integer> nums = new ArrayList<>();
        int tmp = 1;
        int cont = 0;
        for (String s:str.split("")){
            if (Integer.parseInt(s)== tmp){
                cont++;
            } else {
                nums.add(cont);
                cont = 1;
                tmp = 1 - tmp;
            }
        }
        if (cont != 0){
            nums.add(cont);
        }
        if (nums.size() % 2 == 0){
            nums.add(0);
        }
        Integer[] nums_ = nums.toArray(new Integer[nums.size()]);
        int ans = 0;
        ArrayList<Integer> list = new ArrayList<>();
        int k = K * 2 + 1;
        for (int i=0;i<nums_.length;i+=2){
            for (int j=i;j<Math.min(i+k,nums_.length);j++){
                ans += nums_[j];
            }
            list.add(ans);
            ans = 0;
        }
        for (int i:list){
            if (ans < i){
                ans = i;
            }
        }
        System.out.println(ans);
    }
}