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: Wrong Answer)

using System;
using System.IO;
using System.Linq;

class Program
{
    static void Solve()
    {
        var inputs = ReadInts();
        var N = inputs[0]; // N文字
        var K = inputs[1]; // K回
        var S = Read();

        var pattern = new int[N];
        pattern[0] = 0;
        var curChar = '1';
        var cur = 0;

        for (var i = 0; i < N; i++)
        {
            if (S[i] == curChar)
            {
                pattern[cur]++;
            }
            else
            {
                cur++;
                pattern[cur] = 1;
                curChar = curChar == '0' ? '1' : '0';
            }
        }

        if (curChar == '0')
        {
            cur++;
            pattern[cur] = 0;
        }

        if (cur / 2 <= K)
        {
            Console.WriteLine(N);
            return;
        }

        var ans = new int[cur];
        for (var i = 0; i <= 2 * K; i++)
        {
            ans[0] += pattern[i];
        }

        for (var i = 1; 2 * (i + K) <= cur; i++)
        {
            ans[i] = ans[i - 1] + pattern[2 * (i + K) - 1] + pattern[2 * (i + K)]
                - pattern[2 * (i - 1)] - pattern[2 * i + 1];
        }
        Console.WriteLine(ans.Max());
    }

    static void Main(string[] args)
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        Solve();
        Console.Out.Flush();
    }

    public static string Read() { return Console.ReadLine(); }
    public static int ReadInt() { return int.Parse(Read()); }
    public static long ReadLong() { return long.Parse(Read()); }
    public static double ReadDouble() { return double.Parse(Read()); }

    public static string[] Reads() { return Console.ReadLine().Split(' '); }
    public static int[] ReadInts() { return Reads().Select(_ => int.Parse(_)).ToArray(); }
    public static long[] ReadLongs() { return Reads().Select(_ => long.Parse(_)).ToArray(); }
    public static double[] ReadDoubles() { return Reads().Select(_ => double.Parse(_)).ToArray(); }
}