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.Text.RegularExpressions;
using static System.Console;
public class D
{
  static void Main()
  {
    var input = Array.ConvertAll(ReadLine().Split(), int.Parse);
    var s = ReadLine();

    var addm = false;
    var addb = false;
    if (s[0] == '0')
    {
      s = "1" + s;
      addm = true;
    }
    if (s[s.Length-1] == '0')
    {
      s = s + "1";
      addb = true;
    }
    string[] arr1 = Regex.Split(s, "0+");
    string[] arr2 = Regex.Split(s, "1+");

    var max = 0;
    for (int i = 0; i < arr1.Length - input[1]; i++)
    {
      var temp = arr1[i].Length;
      for (int j = i; j < i + input[1]; j++)
      {
        temp += arr1[j + 1].Length + arr2[j + 1].Length;
      }
      if (i == 0 && addm) temp--;
      if (i == arr1.Length - input[1] && addb) temp--;
      if (max <= temp)
        max = temp;
    }
    WriteLine(max);
  }
}