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-mcs 6.8.0.105) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;
//using System.Windows;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Atcoder
{
    public class Program
    {
        private static long mod = 1000000007;
        private static long max = 999999999999;

        static void Main(string[] args)
        {
            var r = ReadSplit();
            var n = r[0].Long();
            var k = r[1].Long();
            
            var r2 = ReadSplit();
            var pCount = 0;
            var mCount = 0;
            for (int i = 0; i < n; i++)
            {
                if (r2[i].Long() >= 0)
                {
                    pCount++;
                }
                else
                {
                    mCount++;
                }
            }

            var pal = new long[pCount];
            var mal = new long[mCount];

            for (int i = 0; i < n; i++)
            {
                if (r2[i].Long() >= 0)
                {
                    pal[i] = r2[i].Long();
                }
                else
                {
                    mal[i] = r2[i].Long();
                }
            }

            Array.Sort(pal);
            Array.Reverse(pal);
            Array.Sort(mal);
            var useP = 0L;
            var useM = 0L;
            var ans = 1L;
            if (pCount == 0 && k % 2 != 0)
            {
                Array.Reverse(mal);
            }

            for (int i = 0; i < k; i++)
            {
                if (k - i >= 2 && k - useM >= 2)
                {
                    if (pal[useP + 1] == 0)
                    {
                        if (pal[useP] < mal[useM] * mal[useM + 1])
                        {
                            ans *= mal[useM];
                            ans %= mod;
                            ans *= mal[useM + 1];
                            ans %= mod;
                            useM += 2;
                            i++;
                        }
                    }
                    else if (pal[useP] * pal[useP + 1] < mal[useM] * mal[useM + 1])
                    {
                        ans *= mal[useM];
                        ans %= mod;
                        ans *= mal[useM + 1];
                        ans %= mod;
                        useM += 2;
                        i++;
                    }
                    else
                    {
                        ans *= pal[useP];
                        ans %= mod;
                        useP++;
                    }
                }
                else
                {
                    if (pal[useP] != 0)
                    {
                        ans *= pal[useP];
                        ans %= mod;
                        useP++;
                    }
                    else
                    {
                        ans *= mal[useM];
                        ans %= mod;
                        useM++;
                    }
                }
            }
            WriteRead(ans);
        }

        public static string Read()
        {
            return Console.ReadLine();
        }

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

        public static void WriteRead(object str)
        {
            Console.WriteLine(str);
            Read();
        }

        public static void Write(object str)
        {
            Console.WriteLine(str);
        }

        private static bool ChangeMin<T>(ref T a, T b) where T : IComparable
        {
            if (a.CompareTo(b) > 0)
            {
                a = b;
                return true;
            }
            return false;
        }

        private static bool ChangekMax<T>(ref T a, T b) where T : IComparable
        {
            if (b.CompareTo(a) > 0)
            {
                a = b;
                return true;
            }
            return false;
        }

        private static bool NextPermutation(int[] array)
        {
            var size = array.Length;
            var ok = false;

            //array[i]<array[i+1]を満たす最大のiを求める
            int i = size - 2;
            for (; 0 <= i; i--)
            {
                if (array[i] < array[i + 1])
                {
                    ok = true;
                    break;
                }
            }

            //全ての要素が降順の場合、NextPermutationは存在しない
            if (ok == false) return false;

            //array[i]<array[j]を満たす最大のjを求める
            int j = size - 1;
            for (; ; j--)
            {
                if (array[i] < array[j]) break;
            }

            //iとjの要素をswapする
            var tmp = array[i];
            array[i] = array[j];
            array[j] = tmp;

            //i以降の要素を反転させる
            Array.Reverse(array, i + 1, size - (i + 1));

            return true;
        }

        //要素数Nを引数として渡し、0～N-1でできた順列をすべて返す
        static List<int[]> GetAllPermutation(int N)
        {
            var res = new List<int[]>();
            var array = Enumerable.Range(0, N).ToArray();
            do
            {
                var copy = new int[N];
                array.CopyTo(copy, 0);
                res.Add(copy);
            } while (NextPermutation(array));

            return res;
        }

        //配列arrayを引数として渡し,辞書順がarray以上の順列をすべて返す
        static List<int[]> GetAllPermutation(int[] array)
        {
            var size = array.Length;
            var res = new List<int[]>();
            do
            {
                var copy = new int[size];
                array.CopyTo(copy, 0);
                res.Add(copy);
            } while (NextPermutation(array));

            return res;
        }
    }
}


public static class Extentions
{
    public static int Int(this object obj)
    {
        return int.Parse(obj.ToString());
    }

    public static long Long(this object obj)
    {
        return long.Parse(obj.ToString());
    }

    public static decimal Decimal(this object obj)
    {
        return decimal.Parse(obj.ToString());
    }

    public static double Double(this object obj)
    {
        return double.Parse(obj.ToString());
    }

    public static T2 GetValueZero<T1, T2>(this Dictionary<T1, T2> d, T1 key) where T2 : struct
    {
        T2 value;
        if (d.TryGetValue(key, out value))
        {
            return value;
        }
        return new T2();
    }
}