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;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp5
{

    class Program
    {
        static void Main(string[] args)
        {
            string S = Console.ReadLine();
            string[] line = S.Split(' ');
            int N = int.Parse(line[0]);
            int K = int.Parse(line[1]);
            S = Console.ReadLine();
            int sum = 0;
            int ans = 0;
            var list = new List<int>();
            int j = 0;
            list.Add(1);
            for(int i=1; i<N; i++)
            {
                if(S[i] == S[i - 1])
                {
                    list[j]++;
                }
                else
                {
                    list.Add(1);
                    j++;
                }
            }
            if (S[0] == '0')
            {
                list.Insert(0, 0);
            }
            if (S[N-1] == '1')
            {
                list.Add(0);
            }
            j = 0;
            for(int i=0; i<list.Count(); i++)
            {
                if(i <= 2 * K) {
                    sum = sum + list[i];
                    if(sum > ans)
                    {
                        ans = sum;
                    }
                }
                else
                {
                    sum = sum + list[i] - list[j];
                    if(j % 2 == 0 && sum > ans)
                    {
                        ans = sum;
                    }
                    j++;
                }

                Console.WriteLine(ans);

            }


            Console.WriteLine(ans);


        }
    }
}