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: Accepted)

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

namespace D
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = ReadLine().Split(' ');
            int N = int.Parse(input[0]);
            int K = int.Parse(input[1]);
            if(N <= K)
            {
                ReadLine();
                WriteLine(N);
                return;
            }

            var s = ReadLine();

            List<int> index = new List<int>();
            index.Add(0);
            int start = int.Parse(s[0].ToString());
            for(int i = 1; i < N; i++)
            {
                if(s[i] != s[i - 1])
                {
                    index.Add(i);
                }
            }
            index.Add(s.Length);
            List<int> num = new List<int>();
            for(int i=0; i < index.Count; i++)
            {
                num.Add(index[Math.Min((i + (2 * K) + ((i + start) % 2)),index.Count - 1)] - index[i]);
            }

            WriteLine(num.Max());
        }
    }
}