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;

namespace ABC124D
{
    class MainClass
    {

        static int[] n;

        public static void Main(string[] args)
        {

            n = Array.ConvertAll(Console.ReadLine().Split().ToArray(), int.Parse);
            string s = Console.ReadLine();
            int nowl = 0;
            var lrlst = new List<int[]>();
            var lrfst = new int[2] { 0, 0 };
            lrlst.Add(lrfst);
            for (int i = 0; i < s.Length - 1; i++)
            {
                if (s[i] == '0' && s[i + 1] == '1')
                {
                    int[] lr = new int[] { nowl, i + 1 };
                    lrlst.Add(lr);
                }else if (s[i] == '0' && s[i + 1] == '0' && i == s.Length - 2)
                {
                    int[] lr = new int[] { nowl, i + 2 };
                    lrlst.Add(lr);
                }
                else if (s[i] == '1' && s[i + 1] == '0')
                {
                    nowl = i + 1;
                    if (i == s.Length - 2)
                    {
                        int[] lr = new int[] { nowl, i + 2 };
                        lrlst.Add(lr);
                    }

                }
            }
                var lrlast = new int[2] { n[0], 0 };
                lrlst.Add(lrlast);


                /*foreach (int[] lr in lrlst)
                {
                    Console.WriteLine(lr[0] + " " + lr[1]);
                }*/



                int lrcnt = lrlst.Count;
                if (lrcnt - 2 <= n[1])
                {
                    Console.WriteLine(n[0]);
                }
                else
                {
                    int ans = 0;
                    for (int i = 0; i < lrcnt - n[1] - 1; i++)
                    {
                        ans = Math.Max(lrlst[i + n[1] + 1][0] - lrlst[i][1], ans);
                    }
                    Console.WriteLine(ans);
                }
            }
        }
    }