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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;

public class Main {
    public static long MOD = 1000000007;

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        String[] s = br.readLine().split(" ");

        int n = Integer.parseInt(s[0]);
        int k = Integer.parseInt(s[1]);

        String[] s2 = br.readLine().split(" ");
        Integer[] nums = new Integer[n];
        List<Long> positives = new ArrayList<>();
        List<Long> negatives = new ArrayList<>();

        for (int i = 0; i < n; i++) {
            nums[i] = Integer.valueOf(s2[i]);
            int temp = Integer.parseInt(s2[i]);
            if (temp<0)negatives.add((long) temp);
            else if (temp==0){
                System.out.println(0);
                return;
            }
            else  positives.add((long) temp);
        }

        int posCount  = Math.min(k,positives.size());
        int negCount =  k - posCount;

        boolean isPositive = false;
        if(positives.size()==0 && k%2==1){
            Arrays.sort(nums);
            long curr = 1L;
            //for (int i = 0; i < k; i++) {
            for (int i = n-1; i >=n-k; i--) {
                curr = ((curr * nums[i]))%MOD;
            }
            System.out.println((curr+MOD)%MOD);
            return;
        }else if(positives.size()==0 && k%2==0){
            Arrays.sort(nums);
            long curr = 1L;
            //for (int i = n-1; i >=0; i--) {
            for (int i = 0; i < k; i++) {
                curr = (curr * nums[i])%MOD;
            }
            System.out.println((curr)%MOD);
            return;
        }
        if(negCount%2==0)isPositive = true;
        else{
            if (posCount-1>=0 && negCount+1<=negatives.size())isPositive = true; //replace one positive with one negative => negative count = even
            if (posCount+1<=positives.size() && negCount-1>=0)isPositive = true; //replace one negative with another positive => negative count = even
        }

        if (isPositive){
            //positive sing = > select negatives or positives in groups of two (by whichever pair has higher product) and mul 1 more pos at the end if k nos not taken

            positives.sort(Collections.reverseOrder());
            Collections.sort(negatives);

            int negIdx = 0;
            int posIdx = 0;
            int total = k;
            long ans  = 1L;
            if(k%2==1){
                ans = positives.get(posIdx);
                ++posIdx;
                --total;
            }
            while (total>0){

                long negProd = negIdx+1<negatives.size() ? (negatives.get(negIdx)*negatives.get(negIdx+1))%MOD : Long.MIN_VALUE;
                long posProd = posIdx+1<positives.size() ? (positives.get(posIdx)*positives.get(posIdx+1))%MOD : Long.MIN_VALUE;


                ans = (ans * Math.max(negProd,posProd))%MOD;
                if(negProd>posProd)
                    negIdx += 2;
                else
                    posIdx += 2;
                total -= 2;
            }
//            while (total < k && posIdx<positives.size()) {
//                ans = (ans * positives.get(posIdx)) % MOD;
//                ++total;
//                ++posIdx;
//            }
//            while (total < k && negIdx<negatives.size()) {
//                ans = (ans * negatives.get(negIdx)) % MOD;
//                ++total;
//                ++negIdx;
//            }

            System.out.println(ans);
        }else{
            // sign will be negative, hence choose smallest k numbers(by abs value).

            Arrays.sort(nums, (a, b)->Math.abs(a)-Math.abs(b));
            long ans = 1L;
            for(int i = 0 ; i<k; i++){
                ans = (ans*nums[i])%MOD;
            }
            System.out.println((ans+MOD)%MOD);
        }

    }
}