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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.util.*;

/**
 * @author Tran Anh Tai
 * @template for CP codes
 * What a trick prob!
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(in, out);
        out.close();
    }
    // main solver
    static class Task{
        static int MOD = 1000000007;
        public void solve(InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int k = in.nextInt();
            long a[] = new long[n];
            for (int i = 0; i < n; i++){
                a[i] = in.nextLong();
            }
            long result = 1;
            Arrays.sort(a);
            if (a[0] >= 0){
                for (int i = n - 1; i >= n - k; i--){
                    result = (result * a[i]) % MOD;
                }
            }
            else if (a[n - 1] <= 0){
                if (k % 2 == 0){
                    for (int i = 0; i < k; i++){
                        result = ((result * a[i]) % MOD + MOD) % MOD;
                    }
                }
                else{
                    for (int i = n - 1; i >= n - k; i--) {
                        result = ((result * a[i]) % MOD + MOD) % MOD;
                    }
                }
            }
            else{
                int end = n - 1;
                int beg = 0;
                while (k > 1){
                    long x = a[end] * a[end - 1];
                    long y = a[beg] * a[beg + 1];
                    if (x > y){
                        result = ((result * (x % MOD)) % MOD + MOD) % MOD;
                        end -= 2;
                    }
                    else{
                        result = ((result * (y % MOD)) % MOD + MOD) % MOD;
                        beg += 2;
                    }
                    k -= 2;
                }
                if (k == 1){
                    result = ((result * a[end]) % MOD + MOD) % MOD;
                }
            }
            out.println(result);
        }
    }
    // fast input reader class;
    static class InputReader {
        BufferedReader br;
        StringTokenizer st;

        public InputReader(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream));
        }

        public String nextToken() {
            while (st == null || !st.hasMoreTokens()) {
                String line = null;
                try {
                    line = br.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (line == null) {
                    return null;
                }
                st = new StringTokenizer(line);
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(nextToken());
        }
        public long nextLong(){
            return Long.parseLong(nextToken());
        }
    }
}