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;
using System.Collections.Generic;
using System.Text;


public class D
{
	public static void Main()
	{
		string[] args = Console.ReadLine().Split(' ');
		int N = Int32.Parse(args[0]);
		int K = Int32.Parse(args[1]);
		string S = Console.ReadLine();
		
		// 1-0-1-...-0-1
		List<int> nums = new List<int>(N);
		int  now = 1;
		int counter = 0;
		for(int i = 0; i < N; i++)
		{
			if(S[i] == (char)('0' + now))
			{
				counter++;
			}
			else
			{
				nums.Add(counter);
				now = 1 - now;
				counter = 1;
			}			
		}
		if(counter != 0)
			nums.Add(counter);
		
		if(nums.Count % 2 == 0)
			nums.Add(0);
		
		int[] csum = new int[nums.Count + 1];
		for(int i = 0; i < nums.Count; i++)
			csum[i+1] = csum[i] + nums[i];
		
		int result = 0;
		for(int i = 0; i < nums.Count; i+=2)
		{
			int left = i;
			int right = Math.Min(i + 2 * K + 1, nums.Count);
			int tmp = csum[right] - csum[left];

			result = Math.Max(result, tmp);
		}
		
		Console.WriteLine(result);		
	}	
}