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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

public class AtCoder
{

    public static int[] ReadArray()
    {
        return Array.ConvertAll(Console.ReadLine().Split(' '), m => Convert.ToInt32(m));
    }

    public static int ReadInt()
    {
        return Convert.ToInt32(Console.ReadLine());
    }

    public static string ReadStr()
    {
        return Console.ReadLine();
    }

    public static long ReadLong()
    {
        return Convert.ToInt64(Console.ReadLine());
    }

    public static long[] ReadLongArray()
    {
        return Array.ConvertAll(Console.ReadLine().Split(' '), m => Convert.ToInt64(m));

    }


    public static void Main()
    {
        var T = ReadArray();
        var arr = ReadStr();

        int n = T[0], k = T[1];

        int i = 0;

        var q = new Queue<int>();

        int ans = 0;
       
        for (int j = 0; j < n; j++)
        {
            if (arr[j] == '0')
            {
                q.Enqueue(j);
            }

            if (q.Count > k)
            {               
                i = q.Dequeue();
                while (i < n && arr[i] == '0') i++;
            }

            while (j < n && arr[j] == '0')
            {
                j++;                
            }


            ans = Math.Max(ans, j - i + 1);

            

        }

        Console.WriteLine(ans);

       

       

      
       


    }


}