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: Runtime Error)

using System;
using System.Linq;
using System.Collections.Generic;
using static System.Console;

namespace d {
static class Extensions {
   public static int ToInt(this string str) {
      return int.Parse(str);
   }

   public static int[] readIntArr() {
      return ReadLine().Split(' ').Select(int.Parse).ToArray();
   }
}

class Program {
   public static void Main(string[] args) {
      var tmp = Extensions.readIntArr();
      var n = tmp[0];
      var k = tmp[1];
      var s = ReadLine();

      var lst = new List<int>();
      char current = s[0];
      int count = 0;
      for (var i = 1; i < n; i++) {
         if (current != s[i]) {
            current = s[i];
            lst.Add(count);
            count = 0;
         } else {
            count++;
         }
      }

      var arr = lst.ToArray();
      var sum = new int[arr.Length];
      for (var i = 0; i < arr.Length; i++) {
         for (var j = 0; j < 2*k + 1; j++) {
            if ((i + j) < arr.Length) {
               sum[i] += arr[i + j];
            }
         }
      }

      WriteLine(sum.Max());
   }
}

}