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-csc 3.5.0) (judge verdict: Wrong Answer)

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

class Program
{
    public static void Main()
    {
        var n = ReadLine().Split().Select(int.Parse).ToArray();
        var a = ReadLine().Split().Select(long.Parse).ToArray();
        var P = a.Where(x => x > 0).ToArray();
        var N = a.Where(x => x < 0).ToArray();
        if(P.Length + N.Length < n[1])
        {
            WriteLine("0");
            return;
        }
        Sort(P);
        Reverse(P);
        Sort(N);
        if(P.Length == 0)
        {
            Reverse(N);
        }
        Queue<long> numP = new Queue<long>(P);
        Queue<long> numN = new Queue<long>(N);
        int countN = 0;
        long lastN = 0;
        long sum = 1;
        for(int i = 0; i < n[1]; i++)
        {
            if(numP.Count > 0 && numN.Count > 0)
            {
                if(numP.Peek() >= Abs(numN.Peek()))
                {
                    sum = (sum * numP.Dequeue()) % 1000000007;
                }
                else
                {
                    lastN = numN.Dequeue();
                    countN++;
                    sum = (sum * lastN) % 1000000007;
                    while(sum < 0)
                        sum += 1000000007;
                }
            }
            else if(numP.Count > 0)
            {
                sum = (sum * numP.Dequeue()) % 1000000007;
            }
            else if(numN.Count > 0)
            {
                lastN = numN.Dequeue();
                countN++;
                sum = (sum * lastN) % 1000000007;
                while(sum < 0)
                    sum += 1000000007;
            }
        }
        if(countN % 2 == 1 && numP.Count > 0)
        {
            sum = (sum / lastN) % 1000000007;
            sum = (sum * numP.Dequeue()) % 1000000007;
            while(sum < 0)
                sum += 1000000007;
        }
        WriteLine(sum);
        ReadLine();
    }
}