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;
using System.Text;
using System.Threading.Tasks;

static class CodeJam
{
    static int Solve(int N, int K, string S)
    {
        var list = new List<int>();
        for (int i = 0; i < N;)
        {
            int c0 = 0, c1 = 0;
            while (i < N && S[i] == '1') { ++c1; ++i; }
            while (i < N && S[i] == '0') { ++c0; ++i; }
            list.Add(c1);
            list.Add(c0);
        }
        switch (S.Last())
        {
        case '0': list.Add(0); break;
        case '1': list.RemoveAt(list.Count - 1); break;
        }

        if (list.Count <= 3)
        {
            return N;
        }
        else
        {
            int n = Math.Min(list.Count, K * 2 + 1);
            int sum = list.Take(n).Sum();
            int max = sum;
            for (int i = n; i + 1 < list.Count; i += 2)
            {
                sum -= list[i - n];
                sum -= list[i - n + 1];
                sum += list[i];
                sum += list[i + 1];
                max = Math.Max(sum, max);
            }
            return max;
        }
    }

    static void Main(string[] args)
    {
        var V = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        var S = Console.ReadLine();
        Console.WriteLine(Solve(V[0], V[1], S));
    }
}