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: Accepted)

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

namespace AtCoder.E
{
    public class Program
    {
        public static long N { get; private set; }
        public static long K { get; private set; }

        public static void Main() { var r = GetResult(); Debug.WriteLine(r); Console.Write(r); }

        private static object GetResult()
        {
            (N, K) = Read2Longs();
            var A = ReadLongs();

            var zeroCount = 0L;
            var pCount = 0L;
            var mCount = 0L;
            foreach (var a in A)
            {
                if (a == 0) zeroCount++;
                if (a > 0) pCount++;
                if (a < 0) mCount++;
            }

            // ひとつだけ選ぶ場合
            if (K == 1)
            {
                return A.Max();
            }

            // すべて選ぶ場合
            if (N == K)
            {
                var mod = (Modular)A[0];
                for (int i = 1; i < N; i++)
                {
                    mod *= A[i];
                }

                return (int)mod;
            }

            // 0 を選ばざるを得ない場合
            if (K - pCount - mCount > 0) return 0;

            // 負の値になってしまう場合
            if (pCount == 0 && K % 2 == 1)
            {
                if (zeroCount > 0) return 0; // さすがに0の方が大きい
                return GetNegativeMax(A);
            }

            // 正の値にできる場合
            return GetPositiveMax(A);
        }

        private static int GetNegativeMax(List<long> a)
        {
            a = a.OrderByDescending(x => x).ToList();

            // すべて負の値という前提
            var mod = (Modular)a[0];
            for (int i = 1; i < K; i++)
            {
                mod *= a[i];
            }
            return (int)mod;
        }

        private static int GetPositiveMax(List<long> a)
        {
            a = a.OrderByDescending(x => Math.Abs(x)).ToList();

            var isPositive = a[0] > 0;
            var mod = (Modular)Math.Abs(a[0]);
            for (int i = 1; i < K; i++)
            {
                isPositive = isPositive == a[i] > 0;
                mod *= Math.Abs(a[i]);
            }

            if (isPositive)
            {
                return (int)mod;
            }

            // 帳尻合わせが必要
            var pLast = a.Take((int)K).LastOrDefault(x => x > 0);
            var mLast = a.Take((int)K).LastOrDefault(x => x < 0);
            var pFirst = a.Skip((int)K).FirstOrDefault(x => x > 0);
            var mFirst = a.Skip((int)K).FirstOrDefault(x => x < 0);

            if (pLast == 0 || mFirst == 0)
            {
                return (int)(mod / Math.Abs(mLast) * pFirst);
            }

            if (mLast == 0 || pFirst == 0)
            {
                return (int)(mod / pLast * Math.Abs(mFirst));
            }

            //if (Math.Abs(mFirst) / pLast > pFirst / Math.Abs(mLast))
            if (Math.Abs(mFirst) * Math.Abs(mLast) > pLast * pFirst)
            {
                return (int)(mod / pLast * Math.Abs(mFirst));
            }
            else
            {
                return (int)(mod / Math.Abs(mLast) * pFirst);
            }
        }

        #region Console.Read

        public static string ReadText() { return Console.ReadLine(); }
        public static List<string> ReadTexts() { return Console.ReadLine().Split(' ').ToList(); }
        public static long ReadLong() { return long.Parse(Console.ReadLine()); }
        public static (long, long) Read2Longs() { var ls = ReadLongs(); return (ls[0], ls[1]); }
        public static (long, long, long) Read3Longs() { var ls = ReadLongs(); return (ls[0], ls[1], ls[2]); }
        public static (long, long, long, long) Read4Longs() { var ls = ReadLongs(); return (ls[0], ls[1], ls[2], ls[3]); }
        public static (long, long, long, long, long) Read5Longs() { var ls = ReadLongs(); return (ls[0], ls[1], ls[2], ls[3], ls[4]); }
        public static List<long> ReadLongs() { return Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList(); }

        #endregion
    }
    public class Modular
    {
        public long Value { get; private set; }

        private static readonly long _mod = (long)Math.Pow(10, 9) + 7;
        private static readonly List<int> _facCache = new List<int> { 1 };

        public static explicit operator long(Modular m)
        {
            return m.Value;
        }

        public static implicit operator Modular(long a)
        {
            var m = a % _mod;

            return new Modular
            {
                Value = (m < 0) ? m + _mod : m
            };
        }

        public static Modular operator +(Modular a, Modular b)
        {
            return a.Value + b.Value;
        }

        public static Modular operator -(Modular a, Modular b)
        {
            return a.Value - b.Value;
        }

        public static Modular operator *(Modular a, Modular b)
        {
            return a.Value * b.Value;
        }

        public static Modular operator /(Modular a, Modular b)
        {
            return a * Pow(b, _mod - 2);
        }

        public static Modular Pow(Modular a, long n)
        {
            switch (n)
            {
                case 0:
                    return 1;
                case 1:
                    return a;
                default:
                    var p = Pow(a, n / 2);
                    return p * p * Pow(a, n % 2);
            }
        }
        public static Modular Factorial(long n)
        {
            for (var i = _facCache.Count; i <= n; ++i)
            {
                var fac = (int)(Math.BigMul(_facCache.Last(), i) % _mod);
                _facCache.Add(fac);
            }
            return _facCache[(int)n];
        }
        public static Modular Combination(long n, long r)
        {
            Modular ans = 1;
            for (var i = 0; i < r; i++)
            {
                ans *= n - i;
            }
            for (var i = 1; i <= r; i++)
            {
                ans /= i;
            }

            return ans;
        }
        public override string ToString()
        {
            return Value.ToString();
        }
    }
}