Problem:
Score : 500 points

Problem Statement

Given are N integers A_1,\ldots,A_N.

We will choose exactly K of these elements. Find the maximum possible product of the chosen elements.

Then, print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Constraints

1 \leq K \leq N \leq 2\times 10^5

|A_i| \leq 10^9

Input

Input is given from Standard Input in the following format:

N K
A_1 \ldots A_N

Output

Print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Sample Input 1

4 2
1 2 -3 -4

Sample Output 1

12

The possible products of the two chosen elements are 2, -3, -4, -6, -8, and 12, so the maximum product is 12.

Sample Input 2

4 3
-1 -2 -3 -4

Sample Output 2

1000000001

The possible products of the three chosen elements are -24, -12, -8, and -6, so the maximum product is -6.

We print this value modulo (10^9+7), that is, 1000000001.

Sample Input 3

2 1
-1 1000000000

Sample Output 3

1000000000

The possible products of the one chosen element are -1 and 1000000000, so the maximum product is 1000000000.

Sample Input 4

10 10
1000000000 100000000 10000000 1000000 100000 10000 1000 100 10 1

Sample Output 4

999983200

Be sure to print the product modulo (10^9+7).

Solution in C# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.IO;

namespace ABC
{
    class ABC173E
    {
        const string FILE = "/tmp/data.txt";

        static void Main(string[] args)
        {
#if DEBUG
            Console.SetIn(new StreamReader(FILE));
#endif
            var Ia = RIa(2);
            var N = Ia[0];
            var K = Ia[1];            
            Ia = RIa(N);

            List<int> pa = new List<int>();
            List<int> na = new List<int>();

            foreach (int n in Ia)
            {
                if (n >= 0)
                {
                    pa.Add(n);
                }
                else
                {
                    na.Add(n * -1);
                }
            }
            pa.Sort();
            pa.Reverse();
            var pas = pa.ToArray();
            na.Sort();

            if (K % 2 == 1 && pas.Length == 0)
            {
                var nasa = na.ToArray();
                long result = 1;
                for (int i = 0; i < K; ++i)
                {
                    result *= nasa[i];
                    result %= 1000000007;
                }
                result *= -1;
                result += 1000000007;
                Console.WriteLine(result);
                return;
            }
            na.Reverse();
            var nas = na.ToArray();

            long maxResult = long.MinValue;
            for (int nNas = 0; nNas <= nas.Length; nNas += 2)
            {
                long result = 1;
                for (int i = 0; i < nNas; ++i)
                {
                    result *= nas[i];
                    result %= 1000000007;
                }

                for (int i = 0; i < pas.Length && i + nNas < K; ++i)
                {
                    result *= pas[i];
                    result %= 1000000007;
                }

                if (result > maxResult)
                {
                    maxResult = result;
                }
            }
            Console.WriteLine(maxResult);

#if DEBUG
            Console.WriteLine("*** end ***");
            Console.SetIn(Console.In);
            Console.ReadKey();
            Console.WriteLine();
#endif
        }

        static int RI()
        {
            return int.Parse(Console.ReadLine());
        }

        static int[] RIa(int n)
        {
            string[] sa = Console.ReadLine().Split(' ');
            int[] la = new int[n];
            for (int i = 0; i < n; ++i)
            {
                la[i] = int.Parse(sa[i]);
            }
            return la;
        }
    }
}