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.IO;
using System.Linq;
using static System.Math;
using System.Text;
using System.Threading;
using System.Globalization;
using System.Runtime.CompilerServices;
using Library;

namespace Program
{
    public static class ProblemE
    {
        static bool SAIKI = false;
        static public int numberOfRandomCases = 0;
        static public void MakeTestCase(List<string> _input, List<string> _output, ref Func<string[], bool> _outputChecker)
        {
        }
        static public void Solve()
        {
            var N = NN;
            var K = NN;
            var AList = NNList(N);
            var notzero = AList.Where(e => e != 0).ToArray();
            if (notzero.Length < K)
            {
                Console.WriteLine(0);
                return;
            }
            var abssort = notzero.OrderByDescending(e => Abs(e)).ToArray();
            var signCnt = 0L;
            var minsei = long.MaxValue;
            var haveMinsei = false;
            for (var i = 0; i < K; i++)
            {
                if (abssort[i] < 0) ++signCnt;
                if (abssort[i] > 0)
                {
                    minsei = Min(minsei, abssort[i]);
                    haveMinsei = true;
                }
            }
            if (signCnt % 2 == 0)
            {
                LIB_Mod ans = 1;
                for (var i = 0; i < K; i++)
                {
                    ans *= abssort[i];
                }
                Console.WriteLine(ans);
            }
            else
            {
                var maxsei = -1L;
                var maxminus = 0L;
                var haveminus = false;
                for (var i = K; i < abssort.Length; i++)
                {
                    if (abssort[i] > 0)
                    {
                        maxsei = Max(abssort[i], maxsei);
                    }
                    if (abssort[i] < 0)
                    {
                        haveminus = true;
                        if (Abs(maxminus) < Abs(abssort[i]))
                        {
                            maxminus = abssort[i];
                        }
                    }
                }
                if (maxsei == -1)
                {
                    if (haveMinsei && haveminus)
                    {
                        LIB_Mod ans = 1;
                        for (var i = 0; i < K; i++)
                        {
                            ans *= abssort[i];
                        }
                        ans /= minsei;
                        ans *= maxminus;
                        Console.WriteLine(ans);
                    }
                    else
                    {
                        if (notzero.Length != N)
                        {
                            Console.WriteLine(0);
                        }
                        else
                        {
                            LIB_Mod ans = 1;
                            var revsort = notzero.OrderBy(e => Abs(e)).ToArray();
                            for (var i = 0; i < K; i++)
                            {
                                ans *= revsort[i];
                            }
                            Console.WriteLine(ans);
                        }
                    }
                }
                else
                {
                    LIB_Mod ans = 1;
                    var minminus = long.MaxValue;
                    for (var i = 0; i < K; i++)
                    {
                        ans *= abssort[i];
                        if (abssort[i] < 0)
                        {
                            if (Abs(minminus) > Abs(abssort[i]))
                            {
                                minminus = abssort[i];
                            }
                        }
                    }
                    if (haveMinsei && haveminus)
                    {
                        if (Abs(maxminus * minminus) < Abs(maxsei * minsei))
                        {
                            ans /= minminus;
                            ans *= maxsei;
                            Console.WriteLine(ans);
                        }
                        else
                        {
                            ans /= minsei;
                            ans *= maxminus;
                            Console.WriteLine(ans);
                        }
                    }
                    else
                    {
                        ans /= minminus;
                        ans *= maxsei;
                        Console.WriteLine(ans);
                    }
                }
            }

        }
        class Printer : StreamWriter
        {
            public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
            public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { base.AutoFlush = false; }
            public Printer(Stream stream, Encoding encoding) : base(stream, encoding) { base.AutoFlush = false; }
        }
        static LIB_FastIO fastio = new LIB_FastIODebug();
        static public void Main(string[] args) { if (args.Length == 0) { fastio = new LIB_FastIO(); Console.SetOut(new Printer(Console.OpenStandardOutput())); } if (SAIKI) { var t = new Thread(Solve, 134217728); t.Start(); t.Join(); } else Solve(); Console.Out.Flush(); }
        static long NN => fastio.Long();
        static double ND => fastio.Double();
        static string NS => fastio.Scan();
        static long[] NNList(long N) => Repeat(0, N).Select(_ => NN).ToArray();
        static double[] NDList(long N) => Repeat(0, N).Select(_ => ND).ToArray();
        static string[] NSList(long N) => Repeat(0, N).Select(_ => NS).ToArray();
        static long Count<T>(this IEnumerable<T> x, Func<T, bool> pred) => Enumerable.Count(x, pred);
        static IEnumerable<T> Repeat<T>(T v, long n) => Enumerable.Repeat<T>(v, (int)n);
        static IEnumerable<int> Range(long s, long c) => Enumerable.Range((int)s, (int)c);
        static IOrderedEnumerable<T> OrderByRand<T>(this IEnumerable<T> x) => Enumerable.OrderBy(x, _ => xorshift);
        static IOrderedEnumerable<T> OrderBy<T>(this IEnumerable<T> x) => Enumerable.OrderBy(x.OrderByRand(), e => e);
        static IOrderedEnumerable<T1> OrderBy<T1, T2>(this IEnumerable<T1> x, Func<T1, T2> selector) => Enumerable.OrderBy(x.OrderByRand(), selector);
        static IOrderedEnumerable<T> OrderByDescending<T>(this IEnumerable<T> x) => Enumerable.OrderByDescending(x.OrderByRand(), e => e);
        static IOrderedEnumerable<T1> OrderByDescending<T1, T2>(this IEnumerable<T1> x, Func<T1, T2> selector) => Enumerable.OrderByDescending(x.OrderByRand(), selector);
        static IOrderedEnumerable<string> OrderBy(this IEnumerable<string> x) => x.OrderByRand().OrderBy(e => e, StringComparer.OrdinalIgnoreCase);
        static IOrderedEnumerable<T> OrderBy<T>(this IEnumerable<T> x, Func<T, string> selector) => x.OrderByRand().OrderBy(selector, StringComparer.OrdinalIgnoreCase);
        static IOrderedEnumerable<string> OrderByDescending(this IEnumerable<string> x) => x.OrderByRand().OrderByDescending(e => e, StringComparer.OrdinalIgnoreCase);
        static IOrderedEnumerable<T> OrderByDescending<T>(this IEnumerable<T> x, Func<T, string> selector) => x.OrderByRand().OrderByDescending(selector, StringComparer.OrdinalIgnoreCase);
        static uint xorshift { get { _xsi.MoveNext(); return _xsi.Current; } }
        static IEnumerator<uint> _xsi = _xsc();
        static IEnumerator<uint> _xsc() { uint x = 123456789, y = 362436069, z = 521288629, w = (uint)(DateTime.Now.Ticks & 0xffffffff); while (true) { var t = x ^ (x << 11); x = y; y = z; z = w; w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)); yield return w; } }
    }
}
namespace Library {
    class LIB_FastIO
    {
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_FastIO() { str = Console.OpenStandardInput(); }
        readonly Stream str;
        readonly byte[] buf = new byte[1024];
        int len, ptr;
        public bool isEof = false;
        public bool IsEndOfStream
        {
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            get { return isEof; }
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        byte read()
        {
            if (isEof) throw new EndOfStreamException();
            if (ptr >= len)
            {
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) <= 0)
                {
                    isEof = true;
                    return 0;
                }
            }
            return buf[ptr++];
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        char Char()
        {
            byte b = 0;
            do b = read();
            while (b < 33 || 126 < b);
            return (char)b;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        virtual public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        virtual public long Long()
        {
            long ret = 0; byte b = 0; var ng = false;
            do b = read();
            while (b != '-' && (b < '0' || '9' < b));
            if (b == '-') { ng = true; b = read(); }
            for (; true; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                else ret = ret * 10 + b - '0';
            }
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        virtual public double Double() { return double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }
    class LIB_FastIODebug : LIB_FastIO
    {
        Queue<string> param = new Queue<string>();
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        string NextString() { if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item); return param.Dequeue(); }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_FastIODebug() { }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override string Scan() => NextString();
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override long Long() => long.Parse(NextString());
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override double Double() => double.Parse(NextString());
    }
    partial struct LIB_Mod : IEquatable<LIB_Mod>, IEquatable<long>
    {
        static public long _mod = 1000000007; long v;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_Mod(long x)
        {
            if (x < _mod && x >= 0) v = x;
            else if ((v = x % _mod) < 0) v += _mod;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public implicit operator LIB_Mod(long x) => new LIB_Mod(x);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public implicit operator long(LIB_Mod x) => x.v;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Add(LIB_Mod x) { if ((v += x.v) >= _mod) v -= _mod; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Sub(LIB_Mod x) { if ((v -= x.v) < 0) v += _mod; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Mul(LIB_Mod x) => v = (v * x.v) % _mod;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Div(LIB_Mod x) => v = (v * Inverse(x.v)) % _mod;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod operator +(LIB_Mod x, LIB_Mod y) { var t = x.v + y.v; return t >= _mod ? new LIB_Mod { v = t - _mod } : new LIB_Mod { v = t }; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod operator -(LIB_Mod x, LIB_Mod y) { var t = x.v - y.v; return t < 0 ? new LIB_Mod { v = t + _mod } : new LIB_Mod { v = t }; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod operator *(LIB_Mod x, LIB_Mod y) => x.v * y.v;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod operator /(LIB_Mod x, LIB_Mod y) => x.v * Inverse(y.v);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public bool operator ==(LIB_Mod x, LIB_Mod y) => x.v == y.v;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public bool operator !=(LIB_Mod x, LIB_Mod y) => x.v != y.v;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public long Inverse(long x)
        {
            long b = _mod, r = 1, u = 0, t = 0;
            while (b > 0)
            {
                var q = x / b;
                t = u;
                u = r - q * u;
                r = t;
                t = b;
                b = x - q * b;
                x = t;
            }
            return r < 0 ? r + _mod : r;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public bool Equals(LIB_Mod x) => v == x.v;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public bool Equals(long x) => v == x;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override bool Equals(object x) => x == null ? false : Equals((LIB_Mod)x);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override int GetHashCode() => v.GetHashCode();
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override string ToString() => v.ToString();
        static List<LIB_Mod> _fact = new List<LIB_Mod>() { 1 };
        static long _factm = _mod;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static void B(long n)
        {
            if (_factm != _mod) _fact = new List<LIB_Mod>() { 1 };
            if (n >= _fact.Count)
                for (int i = _fact.Count; i <= n; ++i)
                    _fact.Add(_fact[i - 1] * i);
            _factm = _mod;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod Comb(long n, long k)
        {
            B(n);
            if (n == 0 && k == 0) return 1;
            if (n < k || n < 0) return 0;
            return _fact[(int)n] / _fact[(int)(n - k)] / _fact[(int)k];
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod CombOK(long n, long k)
        {
            LIB_Mod ret = 1;
            for (var i = 0; i < k; i++) ret *= n - i;
            for (var i = 1; i <= k; i++) ret /= i;
            return ret;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod Perm(long n, long k)
        {
            B(n);
            if (n == 0 && k == 0) return 1;
            if (n < k || n < 0) return 0;
            return _fact[(int)n] / _fact[(int)(n - k)];
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public LIB_Mod Pow(LIB_Mod x, long y)
        {
            LIB_Mod a = 1;
            while (y != 0)
            {
                if ((y & 1) == 1) a.Mul(x);
                x.Mul(x);
                y >>= 1;
            }
            return a;
        }
    }
}