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

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

        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;
            }

            a = a.OrderByDescending(x => Math.Abs(x)).ToArray();

            bool positive = true;
            int nlast = 0;
            int plast = -1;
            for (int i = 0; i < k; i++)
            {
                if (a[i] < 0)
                {
                    positive = !positive;
                    nlast = i;
                }
                else
                    plast = i;
            }

            // 上位K個の積が正なら
            if (positive)
            {
                for (int i = 0; i < k; i++)
                    ans = ans * (a[i] > 0 ? a[i] : (mod + a[i])) % mod;
                Console.WriteLine(ans);
                return;
            }

            int nalt = -1;
            for (int i = k; i < a.Length; i++)
            {
                if (a[i] >= 0)
                {
                    nalt = i;
                    break;
                }
            }

            int palt = -1;
            for (int i = k; i < a.Length; i++)
            {
                if (a[i] < 0)
                {
                    palt = i;
                    break;
                }
            }

            if (plast >= 0 && palt >= 0)
            {
                if (nlast >= 0 && nalt >= 0)
                {
                    if (a[palt] * a[nlast] > a[nalt] * a[plast])
                        ans = Prod(a, k, plast, palt);
                    else
                        ans = Prod(a, k, nlast, nalt);
                }
                else
                    ans = Prod(a, k, plast, palt);
            }
            else
                ans = Prod(a, k, nlast, nalt);
            Console.WriteLine(ans);
        }

        static long Prod(long[] a, int k, int skip, int alt)
        {
            long ans = (mod + a[alt]) % mod;
            for (int i = 0; i < k; i++)
                if (i != skip)
                    ans = ans * (mod + a[i]) % mod;
            return ans;
        }
    }
}