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.Linq;
using System.Collections.Generic;
class c
{
    static void Main()
    {
        var nk = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        int n = nk[0], k = nk[1];
        var s = Console.ReadLine();
        int cnt = 1;
        long temp = 0;
        var list = new List<long>();
        long ans = 0;
        for (int i = 1; i < s.Length; i++)
        {
            if (s[i] == s[i - 1]) cnt++;
            else
            {
                list.Add(cnt);
                cnt = 1;
            }
        }
        list.Add(cnt);
        var remover = list.ToList();

        if (s[0] == '0')
        {
            k = k * 2;
            for (int i = 0; i < list.Count; i++)
            {
                temp += list[i];
                if (i % 2 == 1) ans = Math.Max(ans, temp);
                if (k <= 0)
                {
                    temp -= remover[0];
                    remover.RemoveAt(0);
                }
                else k--;
                if (i % 2 == 0) ans = Math.Max(ans, temp);
            }
        }
        else
        {
            k = k * 2 + 1;
            for (int i = 0; i < list.Count; i++)
            {
                temp += list[i];
                if (k <= 0 && i % 2 == 1)
                {
                    temp -= remover[0];
                    remover.RemoveAt(0);
                    temp -= remover[0];
                    remover.RemoveAt(0);
                }
                else k--;
                ans = Math.Max(ans, temp);
            }
        }

        Console.WriteLine(ans);
    }
}