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.Linq;
using System.Collections.Generic;

namespace Algorithm
{
    class Program
    {
        static void Main(string[] args)
        {
            var l = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int N = l[0], K = l[1];

            var array = Console.ReadLine().ToCharArray();
            var acum = new List<int>();
            if (array[0] == '0') acum.Add(0);

            for (var i = 0; i < array.Count();)
            {
                var count = i;
                while (count < array.Count() && array[count] == array[i]) count++;
                acum.Add(count - i);
                i = count;
            }
            if (array[N - 1] == '0') acum.Add(0);

            var sum = new long[acum.Count()+1];
            for (var i = 0; i < acum.Count(); i++) sum[i + 1] = sum[i] + acum[i];

            var res = 0L;
            for (var left = 0; left < sum.Count(); left += 2)
            {
                var right = left + K * 2 + 1;
                if (right >= sum.Count()) right = sum.Count() - 1;
                res = Math.Max(res, sum[right] - sum[left]);
            }
            Console.WriteLine(res);
        }
    }
}