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.Linq;
using System.IO;
using System.Threading;
using System.Runtime.CompilerServices;
using System.Text;
using System.Diagnostics;
using System.Numerics;
using static System.Console;
using static System.Convert;
using static System.Math;
using static Template;
using Pi = Pair<int, int>;

class Solver
{
    public Scanner sc;
    public void Solve()
    {
        int N, K;
        sc.Make(out N, out K);
        var A = sc.ArrInt;
        if (N == K) Fail(A.Aggregate((ModInt)1, (a, b) => a * b));
        if (K == 1) Fail(A.Max());
        Array.Sort(A, (a, b) => Abs(b).CompareTo(Abs(a)));
        var s = 1;ModInt res = 1;var lasm = -1;var lasp = -1;
        for(int i = 0; i < K - 1; i++)
        {
            res *= (ModInt)A[i];if (A[i] < 0) { s *= -1; lasm = i; } else lasp = i;
        }
        if (s == -1)
        {
            var B = (long)A[lasm]; var C = 1L;
            var ct = 0; var cm = 0;
            for (int i = K - 1; i < N; i++)
            {
                if (A[i] > 0 && ct < 2) { C *= A[i]; ct++; }
                if (A[i] < 0 && cm < 1) { B *= A[i]; cm++; }
            }
            res /= (ModInt)A[lasm];
            if (B > C) res *= B;
            else res *= C;
            Fail(res);
        }
        else
        {
            if (lasp == -1)
            {
                var ok = true;
                for (int j = K - 1; j < N; j++)
                    if (A[j] > 0) { res *= A[j]; ok = false;break; }
                if (!ok) Fail(res);
            }
            else
            {
                var B = 1L; var C = 1L;
                C *= A[lasp]; var ct = 0; var cm = 0;
                for (int i = K - 1; i < N; i++)
                {
                    if (A[i] > 0 && ct < 1) { C *= A[i]; ct++; }
                    if (A[i] < 0 && cm < 2) { B *= A[i]; cm++; }
                }

                res /= A[lasp];
                if (B < C) res *= C;
                else res *= B;
                Fail(res);
            }
        }
        Console.WriteLine(A.Reverse().Take(K).Aggregate((ModInt)1, (a, b) => a * b));

    }
}


public struct ModInt
{
    public const long MOD = (int)1e9 + 7;
    //public const long MOD = 998244353;
    public long Value { get; set; }
    public ModInt(long n = 0) { Value = n; }
    private static ModInt[] fac;//i!
    private static ModInt[] inv;//1/i
    private static ModInt[] facinv;//1/(i!)
    public override string ToString() => Value.ToString();
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator +(ModInt l, ModInt r)
    {
        l.Value += r.Value;
        if (l.Value >= MOD) l.Value -= MOD;
        return l;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator -(ModInt l, ModInt r)
    {
        l.Value -= r.Value;
        if (l.Value < 0) l.Value += MOD;
        return l;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator *(ModInt l, ModInt r) => new ModInt(l.Value * r.Value % MOD);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt operator /(ModInt l, ModInt r) => l * Pow(r, MOD - 2);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static implicit operator long(ModInt l) => l.Value;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static implicit operator ModInt(long n)
    {
        n %= MOD; if (n < 0) n += MOD;
        return new ModInt(n);
    }

    public static ModInt Pow(ModInt m, long n)
    {
        if (n == 0) return 1;
        if (n % 2 == 0) return Pow(m * m, n >> 1);
        else return Pow(m * m, n >> 1) * m;
    }

    public static void Build(int n)
    {
        fac = new ModInt[n + 1];
        facinv = new ModInt[n + 1];
        inv = new ModInt[n + 1];
        inv[1] = 1;
        fac[0] = fac[1] = 1;
        facinv[0] = facinv[1] = 1;
        for (var i = 2; i <= n; i++)
        {
            fac[i] = fac[i - 1] * i;
            inv[i] = MOD - inv[MOD % i] * (MOD / i);
            facinv[i] = facinv[i - 1] * inv[i];
        }
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt Fac(ModInt n) => fac[n];
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt Inv(ModInt n) => inv[n];
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt FacInv(ModInt n) => facinv[n];
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static ModInt Comb(ModInt n, ModInt r)
    {
        if (n < r) return 0;
        if (n == r) return 1;
        var calc = fac[n];
        calc = calc * facinv[r];
        calc = calc * facinv[n - r];
        return calc;
    }
}
#region Template
public static class Template
{
    static void Main(string[] args)
    {
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        var sol = new Solver() { sc = new Scanner() };
        //var th = new Thread(sol.Solve, 1 << 26);th.Start();th.Join();
        sol.Solve();
        Console.Out.Flush();
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmin<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) > 0) { a = b; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmax<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) < 0) { a = b; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static void swap<T>(ref T a, ref T b) { var t = b; b = a; a = t; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static void swap<T>(this IList<T> A, int i, int j) { var t = A[i]; A[i] = A[j]; A[j] = t; }
    public static T[] Create<T>(int n, Func<T> f) { var rt = new T[n]; for (var i = 0; i < rt.Length; ++i) rt[i] = f(); return rt; }
    public static T[] Create<T>(int n, Func<int, T> f) { var rt = new T[n]; for (var i = 0; i < rt.Length; ++i) rt[i] = f(i); return rt; }
    public static IEnumerable<T> Shuffle<T>(this IEnumerable<T> A) => A.OrderBy(v => Guid.NewGuid());
    public static int CompareTo<T>(this T[] A, T[] B, Comparison<T> cmp = null) { cmp = cmp ?? Comparer<T>.Default.Compare; for (var i = 0; i < Min(A.Length, B.Length); i++) { int c = cmp(A[i], B[i]); if (c > 0) return 1; else if (c < 0) return -1; } if (A.Length == B.Length) return 0; if (A.Length > B.Length) return 1; else return -1; }
    public static int ArgMax<T>(this IList<T> A, Comparison<T> cmp = null) { cmp = cmp ?? Comparer<T>.Default.Compare; T max = A[0]; int rt = 0; for (int i = 1; i < A.Count; i++) if (cmp(max, A[i]) < 0) { max = A[i]; rt = i; } return rt; }
    public static T PopBack<T>(this List<T> A) { var v = A[A.Count - 1]; A.RemoveAt(A.Count - 1); return v; }
    public static void Fail<T>(T s) { Console.WriteLine(s); Console.Out.Close(); Environment.Exit(0); }
}
public class Scanner
{
    public string Str => Console.ReadLine().Trim();
    public int Int => int.Parse(Str);
    public long Long => long.Parse(Str);
    public double Double => double.Parse(Str);
    public int[] ArrInt => Str.Split(' ').Select(int.Parse).ToArray();
    public long[] ArrLong => Str.Split(' ').Select(long.Parse).ToArray();
    public char[][] Grid(int n) => Create(n, () => Str.ToCharArray());
    public int[] ArrInt1D(int n) => Create(n, () => Int);
    public long[] ArrLong1D(int n) => Create(n, () => Long);
    public int[][] ArrInt2D(int n) => Create(n, () => ArrInt);
    public long[][] ArrLong2D(int n) => Create(n, () => ArrLong);
    private Queue<string> q = new Queue<string>();
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public T Next<T>() { if (q.Count == 0) foreach (var item in Str.Split(' ')) q.Enqueue(item); while (q.Peek() == "") q.Dequeue(); return (T)Convert.ChangeType(q.Dequeue(), typeof(T)); }
    public void Make<T1>(out T1 v1) => v1 = Next<T1>();
    public void Make<T1, T2>(out T1 v1, out T2 v2) { v1 = Next<T1>(); v2 = Next<T2>(); }
    public void Make<T1, T2, T3>(out T1 v1, out T2 v2, out T3 v3) { Make(out v1, out v2); v3 = Next<T3>(); }
    public void Make<T1, T2, T3, T4>(out T1 v1, out T2 v2, out T3 v3, out T4 v4) { Make(out v1, out v2, out v3); v4 = Next<T4>(); }
    public void Make<T1, T2, T3, T4, T5>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5) { Make(out v1, out v2, out v3, out v4); v5 = Next<T5>(); }
    public void Make<T1, T2, T3, T4, T5, T6>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6) { Make(out v1, out v2, out v3, out v4, out v5); v6 = Next<T6>(); }
    public void Make<T1, T2, T3, T4, T5, T6, T7>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6, out T7 v7) { Make(out v1, out v2, out v3, out v4, out v5, out v6); v7 = Next<T7>(); }
    //public (T1, T2) Make<T1, T2>() { Make(out T1 v1, out T2 v2); return (v1, v2); }
    //public (T1, T2, T3) Make<T1, T2, T3>() { Make(out T1 v1, out T2 v2, out T3 v3); return (v1, v2, v3); }
    //public (T1, T2, T3, T4) Make<T1, T2, T3, T4>() { Make(out T1 v1, out T2 v2, out T3 v3, out T4 v4); return (v1, v2, v3, v4); }
}
public class Pair<T1, T2> : IComparable<Pair<T1, T2>>
{
    public T1 v1;
    public T2 v2;
    public Pair() { }
    public Pair(T1 v1, T2 v2)
    { this.v1 = v1; this.v2 = v2; }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public int CompareTo(Pair<T1, T2> p)
    {
        var c = Comparer<T1>.Default.Compare(v1, p.v1);
        if (c == 0)
            c = Comparer<T2>.Default.Compare(v2, p.v2);
        return c;
    }
    public override string ToString() => $"{v1.ToString()} {v2.ToString()}";
    public void Deconstruct(out T1 a, out T2 b) { a = v1; b = v2; }

    public static implicit operator Pair<T1,T2>((T1 f, T2 s) p) => new Pair<T1, T2>(p.f, p.s);
}

public class Pair<T1, T2, T3> : Pair<T1, T2>, IComparable<Pair<T1, T2, T3>>
{
    public T3 v3;
    public Pair() : base() { }
    public Pair(T1 v1, T2 v2, T3 v3) : base(v1, v2)
    { this.v3 = v3; }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public int CompareTo(Pair<T1, T2, T3> p)
    {
        var c = base.CompareTo(p);
        if (c == 0)
            c = Comparer<T3>.Default.Compare(v3, p.v3);
        return c;
    }
    public override string ToString() => $"{base.ToString()} {v3.ToString()}";
    public void Deconstruct(out T1 a, out T2 b, out T3 c) { Deconstruct(out a, out b); c = v3; }

    public static implicit operator Pair<T1, T2, T3>((T1 f, T2 s, T3 t) p) => new Pair<T1, T2, T3>(p.f, p.s, p.t);
}
#endregion