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.Generic;
using System.Linq;

class Program
{
    static void Main()
    {
        Console.WriteLine(Solve());
        return;
    }

    public static string Solve()
    {
        int ans = 0;
        int[] input = ReadInts();
        int N = input[0];
        int K = input[1];
        string S = Read();
        List<int> nums = new List<int>();
        int i = 0, sum0 = 0,sum1 = 0,max = 0;
        while (i < N && S[i] == '1')
        {
            i++;
            sum1++;
        }
        max += sum1;
        while (i < N)
        {
            while (i < N && S[i] == '0')
            {
                i++;
                sum0++;
            }
            nums.Add(sum0 + sum1);
            max += sum0;
            sum0 = 0;
            sum1 = 0;
            while (i < N && S[i] == '1')
            {
                i++;
                sum1++;
            }
            max += sum1;
            if (nums.Count > K)
            {
                max -= nums[0];
                nums.RemoveAt(0);
            }
            ans = Math.Max(ans, max);
        }
        ans = Math.Max(ans, max);
        return ans.ToString();
    }

    private static string Read() { return Console.ReadLine(); }
    private static int ReadInt() { return int.Parse(Read()); }
    private static long ReadLong() { return long.Parse(Read()); }
    private static double ReadDouble() { return double.Parse(Read()); }
    private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
    private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
    private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
}