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.Linq;
using System.Collections.Generic;
using static System.Math;
using System;

public class Hello
{
    public static void Main()
    {
        string[] line = Console.ReadLine().Trim().Split(' ');
        var n = int.Parse(line[0]);
        var k = int.Parse(line[1]);
        var s = Console.ReadLine().Trim();
        if (n == 1 ) { Console.WriteLine(1); goto exit; }
        var a = s.ToCharArray();
        var b = new List<int>();
        if (a[0] == '0') b.Add(0);
        var t = a[0];
        var count = 1;
        for (int i = 1; i < n; i++)
        {
            if (a[i] == t) count++;
            else
            {
                b.Add(count);
                count = 1;
            }
            t = a[i];
        }
        b.Add(count);
        var x = 2 * k + 1;
        for (int i = 0; i < x + 1; i++) b.Add(0);
        var bc = b.Count();
        var c = new int[bc+ 1];
        for (int i = 1; i < bc + 1; i++)
            c[i] = c[i - 1] + b[i - 1];
        var ans = 0;
        for (int i = 0; i <= c.Length - x -1 ; i+=2)
        {
            var tt = c[i + x ] - c[i];
            ans = Max(ans, tt);
        }
        Console.WriteLine(ans);
        exit:;
    }
}