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)

#if DEBUG
using Console = AtCoder.Console;
#endif
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder
{
    class Program
    {
        static void Main()
        {
#if DEBUG
            Console.Arg =
@"1 1
1
";
#endif
            var k = Console.ReadLine().Split(' ')[1].ToInt();
            var s = Console.ReadLine();
            var nums = new List<int>(s.Length);
            nums.Add(0);
            char current = s[0];
            for(int i = 0; i < s.Length; i++) {
                if(s[i] == current) {
                    nums[nums.Count - 1]++;
                }
                else {
                    nums.Add(1);
                    current = s[i];
                }
                
            }
            var ans = new int[nums.Count];
            var p = k % 2;
            var l = 2 * k + 1;
            for(int i = 0; i < nums.Count; i++) {
                if(s[0].ToString().ToInt() + p % 2 == i % 2) { continue; }
                for(int j = 0; j < l; j++) {
                    var index = i - k + j;
                    if(index < 0 || index >= nums.Count) { continue; }
                    ans[i] += nums[index];
                }
            }
            Console.WriteLine(ans.Max());
#if DEBUG
            Console.Wait();
#endif

        }
    }

    public static class StringExtension
    {
        public static int ToInt(this string str) => int.Parse(str);

        public static long ToLong(this string str) => long.Parse(str);

        public static short ToShort(this string str) => short.Parse(str);
    }
}