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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ABC124D2
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] input = Console.ReadLine().Split(' ');
            int N = int.Parse(input[0]);
            int K = int.Parse(input[1]);
            string S = Console.ReadLine();
            int upright = 0;//直立している　０
            int onhead = 0;//逆立ちしている　１
            List<int> memo = new List<int>();
            for (int i = 0; i < N; i++)
            {
                if (int.Parse(S.Substring(i, 1)) == 0)
                {
                    if (onhead != 0) memo.Add(onhead);
                    onhead = 0;
                    upright++;
                }
                else
                {
                    if (upright != 0) memo.Add(upright);
                    upright = 0;
                    onhead++;
                }
            }
            if (onhead != 0) memo.Add(onhead);
            if (upright != 0) memo.Add(upright);
            List<int> cumulative = new List<int>();//累積和を求める
            int c = 0;
            if (int.Parse(S.Substring(0, 1)) == 1)//1から始まるとき
            {
                cumulative.Add(c);
                for (int i = 0; i < memo.Count; i++)
                {
                    cumulative.Add(c+=memo[i]);
                }
            }
            else //0から始まるとき
            {
                cumulative.Add(c);
                cumulative.Add(c);
                for (int i = 0; i < memo.Count; i++)
                {
                    cumulative.Add(c+=memo[i]);
                }
                cumulative.Add(c);
            }
                /*
                foreach (var item in cumulative)
                {
                    Console.Write(item + " ");
                }
                Console.WriteLine();
                */
                List<int> answers = new List<int>();
                int candidate = 0;
                int max = 1;
            for (int j = 1; j <= K; j++)
            {
                for (int i = 0; i < (cumulative.Count-j*2)/2; i++)
                {
                    candidate = cumulative[i*2 + j*2+1] - cumulative[i*2];
                    if (max < candidate) max = candidate;
                    answers.Add(max);
                    //Console.WriteLine(candidate);
                }
            }
            Console.WriteLine(max);
        }
    }
}