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: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.Collections;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Sparsh Sanchorawala
 */
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);
        EMultiplication4 solver = new EMultiplication4();
        solver.solve(1, in, out);
        out.close();
    }

    static class EMultiplication4 {
        public void solve(int testNumber, InputReader s, PrintWriter w) {
            int n = s.nextInt(), k = s.nextInt();
            int zero = 0;
            long[] a = new long[n];
            ArrayList<Long> neg = new ArrayList<>();
            ArrayList<Long> pos = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                a[i] = s.nextLong();
                if (a[i] < 0) {
                    neg.add(a[i]);
                } else if (a[i] > 0) {
                    pos.add(a[i]);
                } else
                    zero++;
            }

            Collections.sort(neg);
            Collections.sort(pos);

            long mod = (long) 1e9 + 7;

            //n = k->, k is odd and no positives
            if (pos.size() == 0 && k % 2 == 1) {
                if (zero > 0) {
                    w.println(0);
                    return;
                }
                long res = 1;
                for (int i = 0; i < k; i++)
                    res = res * ((neg.get(neg.size() - 1 - i) + mod) % mod) % mod;
                w.println(res);
                return;
            }

            if (n == k & neg.size() % 2 == 1) {
                if (zero > 0) {
                    w.println(0);
                    return;
                }
                long res = 1;
                for (long x : pos)
                    res = res * x % mod;
                for (long x : neg)
                    res = res * ((x + mod) % mod) % mod;
                w.println(res);
                return;
            }

            if (pos.size() + neg.size() < k) {
                w.println(0);
                return;
            }

            int in = 0, ip = pos.size() - 1;
            long res = 1;
            if (k % 2 == 1) {
                res = res * pos.get(ip) % mod;
                ip--;
                k--;
            }

            while (k > 0 && in + 1 < neg.size() && ip - 1 >= 0) {
                long v1 = neg.get(in) * neg.get(in + 1);
                long v2 = pos.get(ip) * pos.get(ip - 1);

                if (v1 > v2) {
                    res = res * (v1 % mod) % mod;
                    in += 2;
                } else {
                    res = res * (v2 % mod) % mod;
                    ip -= 2;
                }
                k -= 2;
            }

            while (k > 0 && in + 1 < neg.size()) {
                long v1 = neg.get(in) * neg.get(in + 1);
                res = res * (v1 % mod) % mod;
                in += 2;
                k -= 2;
            }

            while (k > 0 && ip - 1 >= 0) {
                long v2 = pos.get(ip) * pos.get(ip - 1);
                res = res * (v2 % mod) % mod;
                ip -= 2;
                k -= 2;
            }

            w.println(res);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}