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: Time Limit Exceeded)

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

class TEST
{
    static int mod = 1000000007;
    static Dictionary<string, long> dic = new Dictionary<string, long>();
    static void Main()
    {
        var inn = Console.ReadLine().Split(' ');
        var n = int.Parse(inn[0]);
        var k = int.Parse(inn[1]);
        var arr = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray(); //new int[] { 1000000000 ,100000000 ,10000000, 1000000 ,100000 ,10000, 1000, 100, 10 ,1 };//Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
        var ans = Mul(arr, k, 1, 0) % mod;
        if (ans < 0)
        {
            Console.Write((ans + mod) % mod);
        }
        else
        {
            Console.Write(ans);
        }

    }

    public static long Mul(int[] arr, int k, long prod, int i)
    {
        string key = k + "|" + prod;
        if (dic.ContainsKey(key))
            return dic[key];
        if (k == 0)
            return (prod) % mod;
        if (i >= arr.Length)
            return int.MinValue % mod;


        var aa = Mul(arr, k - 1, (prod * arr[i]) % mod, i + 1) % mod;
        var bb = Mul(arr, k, prod % mod, i + 1) % mod;

        return dic[key] = Math.Max(aa, bb) % mod;
    }



}