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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;

namespace ConsoleApp
{
    class Program
    {
        static void Main(string[] args)
        {
            var strs = Console.ReadLine().Split();
            var N = int.Parse(strs[0]);
            var K = int.Parse(strs[1]);
            var S = Console.ReadLine();

            if (N == 1)
            {
                Console.WriteLine(1);
                return;
            }

            var line = new List<int>();
            var num = 0;
            for (int i = 0; i < S.Length - 1; i++)
            {
                num++;
                if (S[i] != S[i + 1])
                {
                    line.Add(num);
                    num = 0;
                }
            }
            num++;
            line.Add(num);

            var lineNum = line.Count();
            var groupNum = lineNum - (K * 2);
            var groupLength = new int[groupNum];
            var k21 = K * 2 + 1;

            var topHandStand = S[0] == '1' ? true : false;
            if (topHandStand)
            {
                for (int i = 0; i < k21; i++)
                {
                    groupLength[0] += line[i];
                }
                for (int i = 1; i < groupNum; i++)
                {
                    groupLength[i] = groupLength[i - 1] - line[i - 1] + line[i + K * 2];
                }
            }
            else
            {
                for (int i = 0; i < k21 - 1; i++)
                {
                    groupLength[0] += line[i];
                }
                for (int i = 1; i < groupNum; i++)
                {
                    if (i == 1)
                    {
                        groupLength[i] = groupLength[i - 1] - line[i - 1] + line[i + K * 2 - 1] + line[i + K * 2];
                    }
                    else
                    {
                        groupLength[i] = groupLength[i - 1] - line[i - 1] + line[i + K * 2];
                    }
                }
            }

            Console.WriteLine(groupLength.Max());
        }
    }
}