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 cs
{
    public class Program
    {
        public static void Main(string[] args)
        {
            
            var K = int.Parse(Console.ReadLine().Split(' ')[1]);
            var ho = Console.ReadLine().ToCharArray();
            var input = new int[ho.Length];
            for(int i = 0; i < input.Length; i++){
            	input[i] = int.Parse(ho[i].ToString());
            }
            var count = new int[input.Length];
            int parent = input[0];
            count[0] = (input[0] == 0) ? -1 : 1;
            int zeroCount = (input[0] == 0) ? 1 : 0;
            int oneCount = (input[0] == 0) ? 0 : 1;
            
            int divideCount = 0;
            
            for(int i = 1; i < input.Length; i++){
            	
            	if(input[i] != parent){
            		divideCount++;
            		parent = input[i];
            		if(input[i] == 0){
          				zeroCount++;
          			}else{
          				oneCount++;
          			}
            		count[divideCount] = (input[i] == 0) ? -1 : 1;
            	}else{
            		count[divideCount] += (1 * (count[divideCount] / Math.Abs(count[divideCount])));
            	}
            
            }
            
            count = count.Where(x => x != 0).ToArray();
            if( K > zeroCount) K = zeroCount;
            
            
            if(count[0] < 0){
	        	for(int i = 0; i < count.Length - ((K-1) * 2); i+=2){
	        		if(i == 0){
	        			count[i] = Math.Abs(count[i]);
	        			for(int k = i + 1; k <= i + ((K-1) * 2) + 1; k++){
	        				if(k == count.Length) break;
	        				count[i] += Math.Abs(count[k]);
	        			}
	        		}else{
	        			count[i] = count[i-1] + Math.Abs(count[i]);
	        			for(int k = i + 1; k <= i + ((K-1) * 2) + 1; k++){
	        				if(k == count.Length) break;
	        				count[i] += Math.Abs(count[k]);
	        			}
	        		}
	        	}
        	}else{
				
        		for(int i = 0; i < count.Length - K*2; i+=2){
        			for(int k = i+1; k <= i + (K*2); k++){
        				if(k == count.Length) break;
						//Console.WriteLine(i + "," + k);
        				count[i] += Math.Abs(count[k]);
        			
        			}
        		}
        	
        	}
            
            Console.WriteLine(count.Max());
            
        }
            
            

    }
}