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: Accepted)

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

class Program
{
    static void Main(string[] args)
    {
        string[] line = Console.ReadLine().Split(' ');
        int N = int.Parse(line[0]);
        int K = int.Parse(line[1]);
        char[] input = Console.ReadLine().ToArray();
        List<int> list = new List<int>();
        int now = 1;
        int ct = 0;
        list.Add(0);
        int ans = 0;
        for(int i = 0; i < N; i++)
        {
            if (now == 1 && input[i] == '0')
            {
                now = 0;
                if (ct - K >= 0) { ans = Math.Max(ans, i - list[ct - K]); }
            }
            else if (now == 0 && input[i] == '1')
            {
                now = 1;
                list.Add(i);
                ct++;
            }
        }
        if (now == 1)
        {
            if ((ct - K) >= 0) { ans=Math.Max(ans,N-1-list[ct-K]+1); }
            else { ans = N; }
        }
        else if ((ct - K + 1) >= 0)
        {
            ans = Math.Max(ans, N - 1 - list[ct - K+1] + 1);
        }
        else
        {
            ans = N;
        }
        Console.WriteLine(ans);
    }
}