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

namespace E
{
    public class Program
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var NK = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
            var N = NK[0];
            var K = NK[1];
            var A = Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray();
            var p = (long)1e9 + 7;

            var plus = new List<long>();
            var minus = new List<long>();
            foreach (var a in A)
            {
                if (a >= 0) plus.Add(a);
                else minus.Add(a);
            }

            var ok = false;
            if (plus.Count > 0) ok = N == K ? (minus.Count % 2 == 0) : true;
            else ok = K % 2 == 0;

            var answer = 1L;
            var items = new List<long>();
            if (!ok)
            {
                items = A.OrderBy(x => Math.Abs(x)).Take(K).ToList();
            }
            else
            {
                var pQ = new Queue<long>(plus.OrderByDescending(x => x));
                var mQ = new Queue<long>(minus.OrderBy(x => x));
                if (K % 2 == 1) answer *= pQ.Dequeue();
                items = new List<long>();
                while (pQ.Count() > 1) items.Add((pQ.Dequeue() * pQ.Dequeue()) % p);
                while (mQ.Count() > 1) items.Add((mQ.Dequeue() * mQ.Dequeue()) % p);
                items = items.OrderByDescending(x => x).Take(K / 2).ToList();
            }

            foreach (var item in items)
            {
                answer *= item;
                answer %= p;
            }
            if (answer < 0) answer = (answer + p) % p;
            Console.WriteLine(answer);
        }
    }
}