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;

class ABC124D{
    public static void Main(){
        var NK = Console.ReadLine().Split().Select(int.Parse);
        var Sin = Console.ReadLine().ToCharArray();
        var S = new List<bool>();
        var Si = new List<int>();
        var Sb = new List<bool>();
        var count = 0;
        var bef = Sin[0] == '1';
        for(var index = 0;index<Sin.Length;index++){
            S.Add(Sin[index]=='1');
            if(bef == S.Last()){
                count++;
            }else{
                Si.Add(count);
                Sb.Add(bef);
                bef=S.Last();
                count = 1;
            }
        }
        Si.Add(count);
        Sb.Add(S.Last());
        var max = 0;
        var sum = 0;
        var index2 = 0;
        for(var index = 0;index<Si.Count;index++){
            sum = 0;
            index2 = index;
            count = 0;
            while(index2!=Si.Count){
                if(!Sb[index2])count++;
                if(count>NK.ElementAt(1))break;
                sum += Si[index2];
                index2++;
            }
            if(max<sum)max = sum;
            if(index2 == Si.Count)break;
        }
        Console.WriteLine(max);
    }
}