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.Diagnostics;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static void Main()
    {
        string[] cin = Console.ReadLine().Split();
        int n = int.Parse(cin[0]);
        int k = int.Parse(cin[1]);
        string s = Console.ReadLine();
        List<int> count = new List<int>();
        bool flag = false;
        if (s[0] == '1') flag = true;

        int cnt = 0;
        for (int i = 0; i < n; i++)
        {
            if (flag)
            {
                if (s[i] == '1') cnt++;
                else
                {
                    count.Add(cnt);
                    cnt = 1;
                    flag = !flag;
                }
            }
            else
            {
                if (s[i] == '0') cnt++;
                else
                {
                    count.Add(-cnt);
                    cnt = 1;
                    flag = !flag;
                }
            }
        }
        if (flag) count.Add(cnt);
        else count.Add(-cnt);

        int ans = 0;
        for (int i = 0; i < count.Count; i++)
        {
            int tmp = 0;
            int str = 0;
            int m = i;
            while (m < count.Count)
            {
                if (count[m] > 0) tmp += count[m];
                else
                {
                    if (str == k) break;
                    tmp += -count[m];
                    str++;
                }
                m++;
            }
            ans = Math.Max(ans, tmp);
        }
        if (ans == 0)
        {
            for (int i = 0; i < count.Count; i++)
            {
                if (count[i] > 0) ans += count[i];
                else ans += -count[i];
            }
        }

        Console.WriteLine(ans);
    }
}