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: Runtime Error)

using System;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using System.Text;


class Program
{
    static void Main(string[] args)
    {
        const long mod = 1000000007;

        // 入力
        long[] nk = Console.ReadLine().Split().Select(long.Parse).ToArray();
        long[] a = Console.ReadLine().Split().Select(long.Parse).ToArray();
        var n = nk[0];
        var k = nk[1];

        long ans = 1;

        var p = new List<long>();
        var m = new List<long>();
        for (int i = 0; i < a.Length; i++)
        {
            if (a[i] >= 0) p.Add(a[i]);
            else m.Add(a[i]);
        }

        if (n == k)
        {
            for (int i = 0; i < a.Length; i++)
            {
                ans *= a[i];
                ans %= mod;
            }
        }
        else if (p.Count() == 0)
        {
            m.Sort();
            m.Reverse();
            for (int i = 0; i < k; i++)
            {
                ans *= m[i];
                ans += mod;
                ans %= mod;
            }
        }
        else if (m.Count() == 0)
        {
            p.Sort();
            p.Reverse();
            for (int i = 0; i < k; i++)
            {
                ans *= p[i];
                ans %= mod;
            }
        }
        else if (k == 1)
        {
            ans *= p[p.Count - 1];
            ans %= mod;
        }
        else
        {
            m.Sort();
            p.Sort();
            p.Reverse();

            if (k % 2 == 0)
            {
                var countP = 0;
                var countM = 0;
                while (countP * 2 + countM * 2 < k)
                {
                    if (countM >= m.Count()) countP += 2;
                    else if (countP >= p.Count()) countM += 2;
                    else if (m[countM] * m[countM + 1] > p[countP] * p[countP + 1]) countM += 2;
                    else countP += 2;
                }

                for (int i = 0; i < countP; i++)
                {
                    ans *= p[i];
                    ans %= mod;
                }

                for (int i = 0; i < countM; i++)
                {
                    ans *= m[i];
                    ans %= mod;
                }
            }
            else
            {
                var countP = 1;
                var countM = 0;
                while (countP * 2 + countM * 2 < k)
                {
                    if (countM >= m.Count()) countP += 2;
                    else if (countP >= p.Count()) countM += 2;
                    else if (m[countM] * m[countM + 1] > p[countP] * p[countP + 1]) countM += 2;
                    else countP += 2;
                }

                for (int i = 0; i < countP; i++)
                {
                    ans *= p[i];
                    ans %= mod;
                }

                for (int i = 0; i < countM; i++)
                {
                    ans *= m[i];
                    ans %= mod;
                }
            }
        }

        // 出力
        Console.WriteLine(ans);
    }
}