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 static Input;

public class Prog
{
    private const int INF = 1000000007;
    private const long INFINITY = 9223372036854775807;
    private struct Pair { public int x, y; }
    public static void Main()
    {
        int N = NextInt();
        int K = NextInt();
        string S = NextString();
        List<int> memo = new List<int>();
        int count = 0;
        bool flag = true;
        for (int i = 0; i < N; i++)
        {
            if (!flag && S[i] == '0') { count++; }
            else if (!flag && S[i] == '1') { memo.Add(count); count = 1; flag = true; }
            else if (flag && S[i] == '1') { count++; }
            else if (flag && S[i] == '0') { memo.Add(count); count = 1; flag = false; }
        }
        memo.Add(count);
        if (S[N - 1] == '0') memo.Add(0);
        long ans = memo[0];
        long box = memo[0];
        count = 0;
        for (int i = 1; i < memo.Count(); i += 2)
        {
            count++;
            if (count <= K)
            {
                box += memo[i];
                if (i + 1 != memo.Count()) box += memo[i + 1];
            }
            else
            {
                box += memo[i] + memo[i + 1];
                box -= (memo[i - K * 2] + memo[i - K * 2 - 1]);

            }
            ans = Math.Max(ans, box);
            //count++;
        }
        Console.WriteLine(ans);
    }
}

public class Input
{
    private static Queue<string> q = new Queue<string>();
    private static void Confirm() { if (q.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) q.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(q.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(q.Dequeue()); }
    public static char NextChar() { Confirm(); return char.Parse(q.Dequeue()); }
    public static string NextString() { Confirm(); return q.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(q.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
}