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;
using System.Linq;

class Procon
{
    public Procon() { }
    static void Main(string[] agrs)
    {
        new Procon().Do();
    }

    Scanner cin;

    public void Do()
    {
        cin = new Scanner();

        int N = cin.nextInt();
        int K = cin.nextInt();
        var S = new bool[N];

        for (int i = 0; i < N; i++)
        {
            int c = Console.Read();
            if (c == '0')
            {
                S[i] = false;
            }
            else if (c == '1')
            {
                S[i] = true;
            }
        }

        var ContinuousCount = new List<int>();
        var ContinuousValue = new List<bool>();
        ContinuousCount.Add(1);
        ContinuousValue.Add(S[0]);

        for (int i = 1; i < N; i++)
        {
            if (S[i] == ContinuousValue[ContinuousValue.Count() - 1])
            {
                ContinuousCount[ContinuousCount.Count() - 1]++;
            }
            else
            {
                ContinuousCount.Add(1);
                ContinuousValue.Add(S[i]);
            }
        }

        int max = 0;

        for (int i = 0; i < ContinuousCount.Count(); i++)
        {
            int num;
            if (ContinuousValue[i] == true)
            {
                num = 2 * K + 1;
            }
            else
            {
                num = 2 * K;
            }

            int tmpMax = 0;
            for (int j = 0; j < num; j++)
            {
                if (i + j < ContinuousCount.Count())
                {
                    tmpMax += ContinuousCount[i + j];
                }
            }

            if (tmpMax > max)
            {
                max = tmpMax;
            }
        }

        Console.WriteLine(max);
    }
}

class Scanner
{
    string[] s;
    int i;
    int max_i;

    public Scanner()
    {
        s = new string[0];
        max_i = 0;
        i = 0;
    }

    public string nextString()
    {
        if (i >= s.Length)
        {
            s = Console.ReadLine().Split(' ');
            max_i = s.Length;
            i = 0;
            if (max_i == 0)
            {
                return "";
            }
            return s[i++];
        }
        else
        {
            return s[i++];
        }
    }

    public int nextInt()
    {
        return int.Parse(nextString());
    }

    public long nextLong()
    {
        return long.Parse(nextString());
    }

    public double nextDouble()
    {
        return double.Parse(nextString());
    }

    public string[] arrayString()
    {
        return Console.ReadLine().Split(' ');
    }

    public int[] arrayInt()
    {
        string[] str = Console.ReadLine().Split(' ');
        int[] array = new int[str.Length];
        for (int i = 0; i < str.Length; i++)
        {
            array[i] = int.Parse(str[i]);
        }
        return array;
    }

    public long[] arrayLong()
    {
        string[] str = Console.ReadLine().Split(' ');
        long[] array = new long[str.Length];
        for (int i = 0; i < str.Length; i++)
        {
            array[i] = long.Parse(str[i]);
        }
        return array;
    }

    public double[] arrayDouble()
    {
        string[] str = Console.ReadLine().Split(' ');
        double[] array = new double[str.Length];
        for (int i = 0; i < str.Length; i++)
        {
            array[i] = double.Parse(str[i]);
        }
        return array;
    }
}