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 CompLib.Mathematics;
using CompLib.Util;

public class Program
{
    private int N, K;
    private long[] A;

    public void Solve()
    {
        var sc = new Scanner();
        N = sc.NextInt();
        K = sc.NextInt();
        A = sc.LongArray();

        // 絶対値が大きい順にK個選ぶ

        // 負 偶数個　そのまま
        // 奇数個

        // 奇数減らす 偶数追加

        // 偶数減らす、奇数追加

        Array.Sort(A, (l, r) => Math.Abs(r).CompareTo(Math.Abs(l)));

        int minus = 0;
        int plus = 0;
        bool zero = false;
        ModInt ans = 1;
        for (int i = 0; i < K; i++)
        {
            ans *= A[i];
            if (A[i] > 0) plus++;
            else if (A[i] < 0) minus++;
            else if (A[i] == 0) zero = true;
        }

        if (zero)
        {
            Console.WriteLine(0);
            return;
        }

        if (minus % 2 == 0)
        {
            Console.WriteLine(ans);
            return;
        }

        // マイナス減らす、プラス増やす
        // 
        long minus1 = -1, plus1 = -1;
        long minus2 = -1, plus2 = -1;
        for (int i = K - 1; i >= 0; i--)
        {
            if (A[i] < 0)
            {
                minus1 = A[i];
                break;
            }
        }

        for (int i = K; i < N; i++)
        {
            if (A[i] > 0)
            {
                plus1 = A[i];
                break;
            }
        }


        for (int i = K - 1; i >= 0; i--)
        {
            if (A[i] > 0)
            {
                plus2 = A[i];
                break;
            }
        }

        for (int i = K; i < N; i++)
        {
            if (A[i] < 0)
            {
                minus2 = A[i];
                break;
            }
        }

        bool a = minus1 != -1 && plus1 != -1;
        bool b = minus2 != -1 && plus2 != -1;

        if (a)
        {
            if (b)
            {
                // p1/m1 < m2/p2
                // p1*p2 > m2*m1
                if (plus1 * plus2 > minus2 * minus1)
                {
                    ans *= plus1 * ModInt.Inverse(minus1);
                }
                else
                {
                    ans *= minus2 * ModInt.Inverse(plus2);
                }
            }
            else
            {
                ans *= plus1 * ModInt.Inverse(minus1);
            }
        }
        else
        {
            if (b)
            {
                ans *= minus2 * ModInt.Inverse(plus2);
            }
            else
            {
                ans = 1;
                for (int i = 0; i < K; i++)
                {
                    ans *= A[N - 1 - i];
                }
            }
        }

        Console.WriteLine(ans);
    }

    public static void Main(string[] args) => new Program().Solve();
}

// https://bitbucket.org/camypaper/complib
namespace CompLib.Mathematics
{
    #region ModInt

    /// <summary>
    /// [0,<see cref="Mod"/>) までの値を取るような数
    /// </summary>
    public struct ModInt
    {
        /// <summary>
        /// 剰余を取る値．
        /// </summary>
        public const long Mod = (int) 1e9 + 7;

        /// <summary>
        /// 実際の数値．
        /// </summary>
        public long num;

        /// <summary>
        /// 値が <paramref name="n"/> であるようなインスタンスを構築します．
        /// </summary>
        /// <param name="n">インスタンスが持つ値</param>
        /// <remarks>パフォーマンスの問題上，コンストラクタ内では剰余を取りません．そのため，<paramref name="n"/> ∈ [0,<see cref="Mod"/>) を満たすような <paramref name="n"/> を渡してください．このコンストラクタは O(1) で実行されます．</remarks>
        public ModInt(long n)
        {
            num = n;
        }

        /// <summary>
        /// このインスタンスの数値を文字列に変換します．
        /// </summary>
        /// <returns>[0,<see cref="Mod"/>) の範囲内の整数を 10 進表記したもの．</returns>
        public override string ToString()
        {
            return num.ToString();
        }

        public static ModInt operator +(ModInt l, ModInt r)
        {
            l.num += r.num;
            if (l.num >= Mod) l.num -= Mod;
            return l;
        }

        public static ModInt operator -(ModInt l, ModInt r)
        {
            l.num -= r.num;
            if (l.num < 0) l.num += Mod;
            return l;
        }

        public static ModInt operator *(ModInt l, ModInt r)
        {
            return new ModInt(l.num * r.num % Mod);
        }

        public static implicit operator ModInt(long n)
        {
            n %= Mod;
            if (n < 0) n += Mod;
            return new ModInt(n);
        }

        /// <summary>
        /// 与えられた 2 つの数値からべき剰余を計算します．
        /// </summary>
        /// <param name="v">べき乗の底</param>
        /// <param name="k">べき指数</param>
        /// <returns>繰り返し二乗法により O(N log N) で実行されます．</returns>
        public static ModInt Pow(ModInt v, long k)
        {
            return Pow(v.num, k);
        }

        /// <summary>
        /// 与えられた 2 つの数値からべき剰余を計算します．
        /// </summary>
        /// <param name="v">べき乗の底</param>
        /// <param name="k">べき指数</param>
        /// <returns>繰り返し二乗法により O(N log N) で実行されます．</returns>
        public static ModInt Pow(long v, long k)
        {
            long ret = 1;
            for (k %= Mod - 1; k > 0; k >>= 1, v = v * v % Mod)
                if ((k & 1) == 1)
                    ret = ret * v % Mod;
            return new ModInt(ret);
        }

        /// <summary>
        /// 与えられた数の逆元を計算します．
        /// </summary>
        /// <param name="v">逆元を取る対象となる数</param>
        /// <returns>逆元となるような値</returns>
        /// <remarks>法が素数であることを仮定して，フェルマーの小定理に従って逆元を O(log N) で計算します．</remarks>
        public static ModInt Inverse(ModInt v)
        {
            return Pow(v, Mod - 2);
        }
    }

    #endregion

    #region Binomial Coefficient

    public class BinomialCoefficient
    {
        public ModInt[] fact, ifact;

        public BinomialCoefficient(int n)
        {
            fact = new ModInt[n + 1];
            ifact = new ModInt[n + 1];
            fact[0] = 1;
            for (int i = 1; i <= n; i++)
                fact[i] = fact[i - 1] * i;
            ifact[n] = ModInt.Inverse(fact[n]);
            for (int i = n - 1; i >= 0; i--)
                ifact[i] = ifact[i + 1] * (i + 1);
            ifact[0] = ifact[1];
        }

        public ModInt this[int n, int r]
        {
            get
            {
                if (n < 0 || n >= fact.Length || r < 0 || r > n) return 0;
                return fact[n] * ifact[n - r] * ifact[r];
            }
        }

        public ModInt RepeatedCombination(int n, int k)
        {
            if (k == 0) return 1;
            return this[n + k - 1, k];
        }
    }

    #endregion
}


namespace CompLib.Util
{
    using System;
    using System.Linq;

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            while (_index >= _line.Length)
            {
                _line = Console.ReadLine().Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            _line = Console.ReadLine().Split(Separator);
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}