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.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.Threading.Tasks;
using System.IO;
using System.Diagnostics;
class Program
{
    public static Scanner cin;
    static void Main()
    {
        cin = new Scanner();
        
        int[] nk = cin.arrayInt(2);
        int n = nk[0];
        int k = nk[1];
        string s = ReadLine();
        List<int> renzoku = new List<int>();
        int count = 0;
        int now = 1;
        if (s[0] == "0"[0]) {
            renzoku.Add(0);
            now = 0;
        }
        for (int a = 0; a < n; a++)
        {
            if (now == int.Parse(s[a].ToString())) count++;
            else
            {
                now ^= 1;
                renzoku.Add(count);
                count = 0;
                count++;
            }
            
        }
        renzoku.Add(count);
        if (s[s.Length-1]=="0"[0]) renzoku.Add(0);
        int max = 0;
        for(int a = 0; a < renzoku.Count; a+=2)
        {
            int total = 0;
            int left = a;
            int right = Math.Min(a + k * 2 + 1, renzoku.Count);
            for (int b = left; b < right;b++)
            {
               total += renzoku[b];
            }
            max = Math.Max(max,total);
        }

        WriteLine(max);
        Console.ReadLine();

    }
    static bool search(int[] array,int len,int key)
    {
        for (int a = 0; a < len; a++)
        {
            if (array[a]==key) return true;
        }
        return false;
    }
}





class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string input()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return input();
        i = 0;
        return s[i++];
    }

    public int inputInt()
    {
        return int.Parse(input());
    }
    public int[] arrayInt(int N, int add = 0)
    {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = inputInt() + add;
        }
        return Array;
    }

    public long inputLong()
    {
        return long.Parse(input());
    }

    public long[] arrayLong(int N, long add = 0)
    {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = inputLong() + add;
        }
        return Array;
    }

    public double inputDouble()
    {
        return double.Parse(input());
    }


    public double[] arrayDouble(int N, double add = 0)
    {
        double[] Array = new double[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = inputDouble() + add;
        }
        return Array;
    }
}