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# (Mono-mcs 6.8.0.105) (judge verdict: Wrong Answer)

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

namespace AtCoder
{
    class Program
    {
        private static long mod = 1000000007;
        static void Main(string[] args)
        {
            //var n = long.Parse(ReadLine());
            var line = ReadLine().Split(' ').Select(value => long.Parse(value)).ToArray();
            var n = line[0];
            var k = line[1];

            var aArray = ReadLine().Split(' ').Select(value => new Tuple<long, bool>(long.Parse(value), long.Parse(value) > 0 ? true : false)).ToArray();
            aArray = aArray.Select(value => value.Item1 < 0 ? new Tuple<long, bool>(value.Item1 % mod + mod, value.Item2) : value).OrderByDescending(value => value.Item1).ToArray();

            var positiveNum = aArray.Count(value => value.Item2);
            var zeroNum = aArray.Count(value => value.Item1 == 0);
            var negativeNum = aArray.Length - positiveNum - zeroNum;

            if(k > positiveNum + negativeNum)
            {
                WriteLine(0);
                return;
            }

            var positiveList = new List<long>();
            var negativeList = new List<long>();
            for(var i = 0; i < k; i++)
            {
                if(aArray[i].Item2)
                {
                    positiveList.Add(aArray[i].Item1);
                }
                else
                {
                    negativeList.Add(aArray[i].Item1);
                }
            }

            if(negativeList.Count % 2 == 1 && positiveNum > 0)
            {
                var isPositiveFound = false;
                var isNegativeFound = false;
                for(var i = k; i < aArray.Length; i++)
                {
                    if(aArray[i].Item2 && !isPositiveFound)
                    {
                        positiveList.Add(aArray[i].Item1);
                    }
                    else if(!aArray[i].Item2 && isNegativeFound)
                    {
                        negativeList.Add(aArray[i].Item1);
                    }

                    if(isPositiveFound && isNegativeFound)
                    {
                        break;
                    }
                }

                if(!isNegativeFound)
                {
                    negativeList.RemoveAt(negativeList.Count - 1);
                }
                else if(!isPositiveFound)
                {
                    positiveList.RemoveAt(positiveList.Count - 1);
                }
                else
                {
                    if(positiveList.Count < 2)
                    {
                        positiveList.RemoveAt(positiveList.Count - 1);
                    }
                    else
                    {
                        if(positiveList[positiveList.Count - 2] * positiveList[positiveList.Count - 1] > negativeList[negativeList.Count - 2] * negativeList[negativeList.Count - 1])
                        {
                            negativeList.RemoveAt(negativeList.Count - 1);
                            negativeList.RemoveAt(negativeList.Count - 1);
                        }
                        else
                        {
                            positiveList.RemoveAt(positiveList.Count - 1);
                            positiveList.RemoveAt(positiveList.Count - 1);
                        }
                    }
                }
            }

            long answer = 1;
            foreach(var value in positiveList)
            {
                answer *= value;
                answer %= mod;
            }
            foreach (var value in negativeList)
            {
                answer *= value;
                answer %= mod;
            }

            WriteLine(answer);
        }
    }
}