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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

const int MOD = 1000000007;

int main(void){
    int N, K, Abuf;
    vector<int> Aplus;
    vector<int> Aminus;
    int numAzero = 0;
    cin >> N >> K;
    for(int i=0; i<N; i++){
        cin >> Abuf;
        if(Abuf >= 0)Aplus.push_back(Abuf);
        if(Abuf < 0)Aminus.push_back(Abuf);
    }
    if(Aminus.size() > 1)sort(Aminus.begin(), Aminus.end());
    if(Aplus.size() > 1)sort(Aplus.begin(), Aplus.end(), greater<int>());
    if((Aminus.size() == N)&&(K%2 == 1)){
        long long resMinus = 1LL;
        for(int i=0; i<K; i++){
            resMinus = resMinus * abs(Aminus[N-i-1]) % MOD;
        }
        cout << (MOD - resMinus) % MOD << endl;
    }else{
        long long resPlus = 1LL;
        int countminus = 0;
        int countplus = 0;
        while(countminus + countplus < K){
            if((countminus < (int)Aminus.size()-1)&&(countplus < (int)Aplus.size()-1)&&(countminus + countplus < K-1)){
                if((long long)Aminus[countminus]*Aminus[countminus+1] > (long long)Aplus[countplus]*Aplus[countplus+1]){
                    resPlus = resPlus * abs(Aminus[countminus]) % MOD;
                    resPlus = resPlus * abs(Aminus[countminus+1]) % MOD;
                    countminus += 2;
                }else{
                    resPlus = resPlus * abs(Aplus[countplus]) % MOD;
                    resPlus = resPlus * abs(Aplus[countplus+1]) % MOD;
                    countplus += 2;
                }
            }else if((countminus < (int)Aminus.size()-1)&&(countminus + countplus < K-1)){
                resPlus = resPlus * abs(Aminus[countminus]) % MOD;
                resPlus = resPlus * abs(Aminus[countminus+1]) % MOD;
                countminus += 2;
            }else{
                resPlus = resPlus * abs(Aplus[countplus]) % MOD;
                countplus += 1;
            }
        }
        cout << resPlus << endl;
    }
    return 0;
}