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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.net.ConnectException;
import java.rmi.dgc.Lease;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.NoSuchElementException;
import java.util.Objects;
import java.util.Set;
import java.util.Stack;
import java.util.TreeMap;
import java.util.TreeSet;

import static java.util.Comparator.*;

public class Main {
	public static void main(String[] args) {
		Main main = new Main();
		main.solve();
		main.out.close();
	}
	// ======================================================================
	final long MOD = (int)(1e9) + 7;
	int[] P, M, MX2;
	public void solve() {
		int N = ni();
		int K = ni();
		int[] P = new int[N];
		int[] M = new int[N];
		int[] MX2 = new int[N];
		int sizeP = 0, sizeM = 0, size0 = 0;
		int a;
		long ans = 1;
		for (int i = 0; i < N; i++) {
			a = ni();
			if(a == 0)		size0++;
			else if(a > 0) {
				P[sizeP] = a;
				sizeP++;
			} else {
				M[sizeM] = a;
				sizeM++;
			}
			ans = (ans * a + MOD) % MOD;
		}
		if(K == N) {
			out.println(ans);
			return;
		}
		Arrays.sort(P);
		Arrays.sort(M);
		ans = 1;
		long wk1, wk2;
		if(sizeM == N && K % 2 == 1) {	// マイナスになるので絶対値が小さいものを選ぶ
			while(K > 0) {
				wk1 = sizeP > 0 && N-sizeP >= 0 ? P[N-sizeP] : MOD;
				wk2 = sizeM - 1 >= 0 ? M[sizeM-1] : MOD;
				if(Math.abs(wk1) <= Math.abs(wk2)) {
					ans = (ans * wk1) % MOD;
					sizeP--;
				} else {
					ans = (ans * wk2 + MOD) % MOD;
					sizeM--;
				}
				K--;
			}
			out.println(ans);
			return;
		}
		int cntP = 0, cntM = 0;
		if(K > sizeP + sizeM)		out.println(0);
		else if(K == 1)			out.println(Math.max((sizeP > 0 ? P[N-1] : -MOD), (size0 > 0 ? 0 : M[0])));
		else {							// プラスを作れる
			while(K > 0) {
				if(K > 1) {
					wk1 = (cntM+1 < N ? ((long)M[cntM] * M[cntM+1]) % MOD : 0);
					wk2 = (N-cntP-2 >= 0 ? ((long)P[N-cntP-1] * P[N-cntP-2]) % MOD : 0);
					if(wk1 >= wk2) {
						ans = (ans * wk1) % MOD;
						cntM += 2;
					} else {
						ans = (ans * wk2) % MOD;
						cntP += 2;
					}
					K -= 2;
				} else {
					ans = (ans * P[N-cntP-1]) % MOD;
					K--;
				}
			}
			out.println(ans);
		}
	}

	// ------------------------------------------
	// ライブラリ
	// ------------------------------------------
	// Print
	private PrintWriter out = new PrintWriter(System.out);
	
	// Scanner
	private FastScanner scan = new FastScanner();
	int ni(){ return scan.nextInt();}
	int[] ni(int n){int[] a = new int[n]; for(int i = 0; i < n; i++){a[i] = ni();} return a;}
	int[][] ni(int y, int x){int[][] a = new int[y][x];
	for(int i = 0; i < y; i++){for(int j = 0; j < x; j++){a[i][j] = ni();}} return a;}
	long nl(){return scan.nextLong();}
	long[] nl(int n){long[] a = new long[n]; for(int i = 0; i < n; i++){a[i] = nl();} return a;}
	long[][] nl(int y, int x){long[][] a = new long[y][x];
	for(int i = 0; i < y; i++){for(int j = 0; j < x; j++){a[i][j] = nl();}} return a;}
	String ns(){return scan.next();}
	String[] ns(int n){String[] a = new String[n]; for(int i = 0; i < n; i++){a[i] = ns();} return a;}
	String[][] ns(int y, int x){String[][] a = new String[y][x];
	for(int i = 0; i < y; i++){for(int j = 0; j < x; j++){a[i][j] = ns();}} return a;}
}
class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;
	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		}else{
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}
	private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
	private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
	public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
	public String next() {
		if (!hasNext()) throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while(isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public long nextLong() {
		if (!hasNext()) throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while(true){
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			}else if(b == -1 || !isPrintableChar(b)){
				return minus ? -n : n;
			}else{
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
		return (int) nl;
	}
	public double nextDouble() { return Double.parseDouble(next());}
}