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.Text.RegularExpressions;

namespace kp
{
    public class Program
    {
        //static long[,] cmb;
        static int MAX_INT = 1000000007;
        static void Main(string[] args)
        {
            //int N = Int32.Parse(Console.ReadLine());
            int[] input = Console.ReadLine().Split().Select(p => int.Parse(p)).ToArray();
            int N = input[0];
            int K = input[1];
            string s = Console.ReadLine();

            List<int> people = new List<int>(); // 偶数番目に逆立ちしている人の数、奇数番目に直立している人の数を入れる
            int pp = 0;
            for(int i=0; i<N; i++)
            {
                if(people.Count%2 == 0)
                {
                    // 逆立ちしている人の数を数える
                    if(s[i] == '1')
                    {
                        pp++;
                    }
                    else
                    {
                        people.Add(pp);
                        pp = 1;
                    }
                }
                else
                {
                    // 直立している人の数を数える
                    if(s[i] == '0')
                    {
                        pp++;
                    }
                    else
                    {
                        people.Add(pp);
                        pp = 1;
                    }
                }
            }
            people.Add(pp);
            people.Add(0);

            // 最大K回まで直立している人たちを逆立ちさせる
            int max = 0; // 連続して逆立ちしている人の数の最大値
            pp = s[0] == '0' ? 1 : -1; // 直立0 逆立ち1
            for (int i = 0; 2*i < people.Count; i++ ) // iからi+K-1番目まで
            {
                int sakadachi = people[i]; // 最初の逆立ちしてる人たち
                for(int j = i, kk=0; 2*j+2 < people.Count && kk < K; j++, kk++)
                {
                    // people[2*i+1]から[2*j+1]までの直立している人を逆立ちさせる
                    sakadachi += people[2 * j + 1] + people[2 * j + 2];
                }
                if (max < sakadachi)
                    max = sakadachi;
            }

            Console.WriteLine(max + "");
                
        }
    }
}