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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;

namespace ConsoleApp
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = Console.ReadLine().Split().Select(int.Parse).ToArray();
            var N = input[0];
            var K = input[1];
            var S = Console.ReadLine().ToCharArray();

            var data = CountData(S);
            Console.WriteLine(Ans(data, K));
        }

        static int[] CountData(char[] S)
        {
            var list = new List<int>();

            if (S.First() == '0') list.Add(0);
            var cnt = 1;

            for (int i = 1; i < S.Length; i++)
            {
                if (S[i] != S[i - 1])
                {
                    list.Add(cnt);
                    cnt = 1;
                }
                else
                {
                    cnt++;
                }
            }

            list.Add(cnt);
            if (S.Last() == '0') list.Add(0);

            return list.ToArray();
        }

        static int Ans(int[] data, int K)
        {
            var max = 0;
            var sum = 0;
            for (int i = 0; i <= data.Length / 2; i++)
            {
                var start = 2 * i;
                for (int j = start; j <= Math.Min(data.Length - 1, start + 2 * K); j++)
                {
                    sum += data[j];
                }
                max = Math.Max(sum, max);
                sum = 0;
            }

            return max;
        }
    }
}