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 Handstand
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] a = Console.ReadLine().Split(' ');
            long n = Convert.ToInt64(a[0]);
            long moves = Convert.ToInt64(a[1]);
            string sequence = Console.ReadLine();
            long b = 1;
            int start = 0;
            long max = 0;
            long c = 0;
            long d = 0;
            string temp = "";
            string[] group = new string[n + 1];
            temp = sequence.Substring(0, 1);

            for (int i = 1; i <= n + 1; i++)
            {
                if (n + 1 == i)
                {
                    group[b] = sequence.Substring(start, i - start - 1);
                    break;
                }
                if (temp != sequence.Substring(i - 1, 1))
                {
                    group[b] = sequence.Substring(start, i - start - 1);
                    b++;
                    temp = sequence.Substring(i - 1, 1);
                    start = i - 1;
                }
            }

            if (1 > b - 2 * moves)
            {
                max = n;
            }

            for (long j = 1; j <= b - 2 * moves; j++)
            {
                d = 2 * moves + 1;
                if (b < 2 * moves + 1)
                {
                    max = n;
                    break;
                }
                if (group[j].Substring(0, 1) == "0")
                {
                    d = 2 * moves;
                }

                for (long w = 1; w <= d; w++)
                {
                    c = c + group[w + j - 1].Length;
                }

                if (max < c)
                {
                    max = c;
                }
                c = 0;

            }

            Console.WriteLine(max);
            Console.ReadKey();
        }
    }
}