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: Wrong Answer)

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

class Program
{
    /**
     * 0と1の連続する数を配列に格納する
     * 1010111の場合
     * 0- 0 0
     * 1-1 1 3 => 10103
     * 0を1に変えていけばよいからK=1の場合
     * 0を変えた直後の1の数を数えるので2*1+1回分の1をかぞえる
     * 1010111 => 1110111であれば最初の111で3個
     * 1010111 => 1011111であれば3～7(3+2*1+1-1)を数える
     * 
     * 
     */

    static void Main(string[] args)
    {
        var inputs = Console.ReadLine().Split(' ');
        int N = int.Parse(inputs[0]);
        int K = int.Parse(inputs[1]);
        var S = Console.ReadLine();

        var nums = new List<int>();
        int val = 1;
        int count = 0;
        for(int i = 0; i < N; i++)
        {
            if(S[i] == ('0' + val))
            {
                count++;
            }else
            {
                val = 1 - val;
                nums.Add(count);
                count = 1;
            }
        }
        if (count != 0) nums.Add(count);
        // 0の後ろにある1の数を含めたいので奇数にする
        if (nums.Count % 2 == 0) nums.Add(0);

        var acumSum = new int[nums.Count + 1];
        for(int i = 0; i < nums.Count; i++)
        {
            acumSum[i + 1] = acumSum[i] + nums[i];
        }
        int maxK = 2 * K + 1;
        int max = 0;
        
        for(int i = 0; i < nums.Count; i++)
        {
            int left = i;
            int right = Math.Min(i + maxK, nums.Count);
            max = Math.Max(max, acumSum[right] - acumSum[left]);
        }
        Console.WriteLine(max);
    }



}