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.Linq;

namespace AtCoder.Abc173
{
    class E
    {
        static long mod = 1000000007;

        struct SignedLong
        {
            public long Value;
            public bool Positive;
            public SignedLong(long x)
            {
                if (x < 0)
                {
                    Value = -x;
                    Positive = false;
                }
                else
                {
                    Value = x;
                    Positive = true;
                }
            }
        }

        public static void Main()
        {
            var nk = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            var n = nk[0];
            var k = nk[1];

            long ans = 1;
            var a = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            if (a.All(x => x <= 0) && k % 2 == 1)
            {
                a = a.OrderByDescending(x => x).ToArray();
                for (int i = 0; i < k; i++)
                    ans = (ans * (mod + a[i])) % mod;
                Console.WriteLine(ans);
                return;
            }

            var s = a.Select(x => new SignedLong(x)).OrderByDescending(x => x.Value).ToArray();

            int nn = 0;
            int nlast = 0;
            for (int i = 0; i < k; i++)
            {
                if (!s[i].Positive)
                {
                    nn++;
                    nlast = i;
                }
            }

            if (nn % 2 == 0)
            {
                for (int i = 0; i < k; i++)
                    ans = ans * (s[i].Positive ? s[i].Value : (mod - s[i].Value)) % mod;
            }
            else
            {
                for (int i = 0; i < k; i++)
                {
                    if (i == nlast)
                        continue;
                    ans = ans * (s[i].Positive ? s[i].Value : (mod - s[i].Value)) % mod;
                }
                for (int i = k; i < s.Length; i++)
                {
                    if (s[i].Positive)
                    {
                        ans = ans * s[i].Value % mod;
                        break;
                    }
                }
            }
            Console.WriteLine(ans);
        }
    }
}