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;

namespace atcorder_BeginnerContest_124
{
    class Program
    {

        static void Main(string[] args)
        {

            int[] dataRow = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);

            int len = dataRow[0];
            int cnt = dataRow[1];

            var s = Console.ReadLine().ToArray();

            List<long> cntList = new List<long>();

            char beforeData = '0';
            if ('1' == s[0]) beforeData = '1';

            long tmpCnt = 0;

            for (int i = 0; i < len; i++)
            {
                if (beforeData != s[i])
                {
                    cntList.Add(tmpCnt);
                    if ('1' == beforeData) beforeData = '0';
                    else beforeData = '1';
                }
                tmpCnt++;
            }
            cntList.Add(tmpCnt);
            int listCnt = cntList.Count;

            long ret = 0;
            int idx = 0;

            if ('1' == s[0]) beforeData = '1';
            else beforeData = '0';

            while (idx < listCnt)
            {
                int endIdx = 0;

                if ('1' == beforeData) endIdx = idx + (cnt * 2);
                else endIdx = idx + (cnt * 2) - 1;

                if (listCnt - 1 < endIdx) endIdx = listCnt - 1;

                long tmpRet = cntList[endIdx];
                if (0 <= idx - 1) tmpRet -= cntList[idx - 1];

                if (ret < tmpRet) ret = tmpRet;

                if ('1' == s[idx]) beforeData = '0';
                else beforeData = '1';

                idx++;

            }

            Console.WriteLine(ret);

        }

    }
}