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: Time Limit Exceeded)

using System;
using System.Collections.Generic;

    class Program
    {
        static void Main(string[] args)
        {
            var K = int.Parse(Console.ReadLine().Split(' ')[1]);
            var S = Console.ReadLine();

            var zipS = new List<KeyValuePair<char,int>>();
            var now = S[0];
            var tmpCount = 0;
            for (var i = 0; i < S.Length; i++)
            {
                if(now==S[i])
                {
                    tmpCount++;
                    continue;
                }
                zipS.Add(new KeyValuePair<char, int>(now,tmpCount));
                now = S[i];
                tmpCount = 1;
            }
            zipS.Add(new KeyValuePair<char, int>(now, tmpCount));

            var max = 0;
            var tmpK = K;
            tmpCount = 0;
            for (var i = 0; i < zipS.Count; i++)
            {
                for (var j = i; j < zipS.Count; j++)
                {
                    if(zipS[j].Key == '0')
                    {
                        tmpK--;
                        if (tmpK < 0) break;
                    }
                    tmpCount += zipS[j].Value;
                }
                if (max < tmpCount) max = tmpCount;
                tmpK = K;
                tmpCount = 0;
            }

            Console.WriteLine(max);
        }
    }