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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Reflection;
using System.Runtime.InteropServices.ComTypes;

class MainClass
{
    static void Main()
    {
        var NK = Console.ReadLine().Split().Select(int.Parse).ToArray();
        int N = NK[0];
        int K = NK[1];
        bool[] S = Console.ReadLine().Select(_ => _ == '1').ToArray();
        List<int> d = new List<int> { 0 };

        {
            int i = 0;
            while (i < N && S[i]) i++;
            d.Add(i);
            while (i < N)
            {
                while (i < N && !S[i]) i++;
                while (i < N && S[i]) i++;
                d.Add(i);
            }
        }

        //Console.WriteLine(string.Join(" ",d));
        if (d.Count - 2 <= K) Console.WriteLine(N);
        else
        {
            int l = 0;int r = K;
            int ans = 0;
            while (r < d.Count)
            {
                if (l == 0)
                {
                    ans = Math.Max(d[r] - d[l],ans);
                }
                else
                {
                    ans = Math.Max(d[r] - d[l - 1] - 1, ans);
                }
                l++;r++;
            }

            Console.WriteLine(ans);
        }
    }
}