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)

namespace ABC124_D
{
    using System.Collections;
    using System.Collections.Generic;
    using System.Linq;
    using static System.Console;
    public struct Hoge
    {
        public Hoge(bool handstand, int count)
        {
            Handstand = handstand;
            Count = count;
        }
        public bool Handstand { get; set; }
        public int Count { get; set; }

        public override string ToString() => $"{Handstand} {Count}";
    }
    public class Program
    {
        public static void Main(string[] args)
        {
            var input = ReadInputsAsInt();
            var N = input.Take(1).First();
            var K = input.Take(1).First();
            var S = ReadLine();
            WriteLine(Solve(N, K, S));
        }

        public static int Solve(int n, int k, string s)
        {
            var people = new BitArray(s.Select(c => c == '1').ToArray());

            var list = new List<Hoge>();

            var temp = people[0];
            var count = 1;

            for (int i = 1; i < n; i++)
            {
                if (temp == people[i])
                {
                    count++;
                }
                else
                {
                    list.Add(new Hoge(temp, count));
                    temp = !temp;
                    count = 1;
                }
            }
            list.Add(new Hoge(temp, count));

            if (list.Count == 1) return list[0].Count;

            //var reverseArea = k + 2;
            var first = list[0].Handstand ? 1 : 0;

            var result = 0;
            for (int i = 0; i < list.Where(h => !h.Handstand).Count() - k + 1; i++)
            {
                var indices = Enumerable.Range(0, k).Select(l => first + l * 2);

                var minIndex = first + i * 2;//最小の正立してる人のインデックス
                var maxIndex = first + (i + k - 1) * 2;//最大の正立してる人のインデックス

                var numOfRev = list.Skip(minIndex).Take(maxIndex - minIndex + 1).Select(h => h.Count).Sum();

                if (minIndex > 0) numOfRev += list[minIndex - 1].Count;
                if (maxIndex < list.Count - 1) numOfRev += list[maxIndex + 1].Count;

                if (result < numOfRev) result = numOfRev;
            }

            return result;
        }



        public static IEnumerable<int> ReadInputsAsInt() => ReadLine().Split(' ').Select(x => int.Parse(x));

    }
}