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)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp1
{
	class Program4
	{
		static void Main(string[] args)
		{
			var nk = Console.ReadLine().Split(' ');
			var s = Console.ReadLine();

			List<KeyValuePair<int, int>> numlist = new List<KeyValuePair<int, int>>();

			int k = int.Parse(nk[1]);
			int addk = 0;
			int max = 0;
			int ans = 0;
			bool next = true;
			int num = 0;
			for (int i = 0; i < s.Length; i++)
			{
				bool b = true;
				if (s[i].Equals('1'))
				{
					b = true;
				}
				else
				{
					b = false;
				}

				if (i == 0)
				{
					next = b;
					num++;
					continue;
				}

				// 同じ場合は続く
				if (next.Equals(b))
				{
					num++;
					continue;
				}

				// これは1が続いた
				if (!b)
				{
					numlist.Add(new KeyValuePair<int, int>(1, num));
					ans += num;
					if (ans > max)
					{
						max = ans;
					}
				}
				// ここは0が続いた
				else
				{
					// 0が続いた場合はkを使って裏返す
					if (addk < k)
					{
						addk++;
						numlist.Add(new KeyValuePair<int, int>(0, num));
						ans += num;
						if (ans > max)
						{
							max = ans;
						}
					}
					else
					{
						numlist.Add(new KeyValuePair<int, int>(0, num));
						ans += num;

						// 既にk回裏返している場合はnumlistから0を削除する必要がある
						if (numlist[0].Key == 0)
						{
							ans -= numlist[0].Value;
							numlist.RemoveAt(0);
						}
						else
						{
							ans -= numlist[0].Value;
							ans -= numlist[1].Value;
							numlist.RemoveAt(0);
							numlist.RemoveAt(1);
						}
						addk--;
					}
				}

				next = b;
				num = 1;
			}

			Console.Write(ans.ToString() + "\n");
			//Console.ReadLine();
		}
	}
}