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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
public class ABC
{

    public static void Main(string[] args)
    {
        var split = Console.ReadLine().Split().Select(int.Parse).ToArray();
        int N = split[0];
        int K = split[1];
        string S = Console.ReadLine();

        List<int> list = new List<int>();
        string first = S[0].ToString();
        string looking = first;
        int counter = 0;

        for (int i = 0; i < N; i++)
        {

            if (looking == S[i].ToString()) counter++;
            else
            {
                looking = S[i].ToString();
                list.Add(counter);
                counter = 1;
            }

        }
        list.Add(counter);
        int answer = 0;

        int n_look_array = K * 2 + 1;
        if (first == "0")
        {
            list.Insert(0, 0);

        }
        if (looking == "0")
        {
            list.Add(0);
        }

        n_look_array = K * 2 + 1;


        if (list.Count < n_look_array)
        {
            answer = list.Sum();
        }
        else
        {
            Queue<int> queue = new Queue<int>();
            int sum = 0;
                            queue.Enqueue(list[0]);
                sum += list[0];
                list.RemoveAt(0);
            while (list.Count > 0)
            {
                queue.Enqueue(list[0]);
                sum += list[0];
                list.RemoveAt(0);
                queue.Enqueue(list[0]);
                sum += list[0];
                list.RemoveAt(0);
                if (queue.Count == n_look_array) answer = sum;
                if (queue.Count > n_look_array)
                {
                    sum -= queue.Dequeue();
                    sum -= queue.Dequeue();
                    if (answer < sum) answer = sum;

                }


            }
        }

        Console.WriteLine(answer);
    }
}