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.Text;

class Program
{
	static void Main(string[] args)
	{
		long MOD = 1000000007;
		string[] input = Read();
		int n = int.Parse(input[0]);
		int k = int.Parse(input[1]);
		input = Read();
		long[] friendly = new long[n];
		for(int i=0; i<n; i++) friendly[i] = long.Parse(input[i]);
		Array.Sort(friendly);
		long ans = 1;
		if(k%2==1 && friendly[n-1]<0)
		{
			for(int i=0; i<k; i++) ans *= friendly[n-i-1] % MOD;
			Write(MOD + ans);
			return;			
		}
		if(k%2==1)
		{
			ans = friendly[n-1];
			n--;
			k--;
		}
		int idxPlus = n-1;
		int idxMinus = 0;
		for(int i=0; i<k/2; i++)
		{
			long plus = friendly[idxPlus] * friendly[idxPlus-1];
			long minus = friendly[idxMinus] * friendly[idxMinus+1];
			if(plus>minus)
			{
				ans = (plus % MOD) * ans % MOD;
				idxPlus -= 2; 
			}
			else
			{
				ans = (minus % MOD) * ans % MOD;
				idxMinus += 2;
			}
		}
		if(ans < 0) ans += MOD;
		Write(ans);
	}

	static string[] Read()
	{
		return Console.ReadLine().Split(' ');
	}

	static void Write(object o)
	{
		Console.WriteLine(o.ToString());
	}
}