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 <bits/stdc++.h>

using namespace std;

bool cmp(long long int a, long long int b){
    return abs(a)>abs(b);
}
bool cmp2(long long int a, long long int b){
    return abs(a)<abs(b);
}

long long int tab[200007];

int main()
{
    long long int n, k, i, id=0, iu=0, md=0, mu=0, w=1, ikd=0, iku=0, x=0;
    cin >> n >> k;
    for(i=0; i<n; i++){
        cin >> tab[i];
        if(tab[i]>0){
            id++;
        }
        if(tab[i]<0){
            iu++;
        }
    }
    if(((id==0)&&(k%2))||((k==n)&&(iu%2))){
        sort(tab, tab+n, cmp2);
    }
    else{
        sort(tab, tab+n, cmp);
    }
    for(i=0; i<k; i++){
        if(tab[i]>0){
            if(md!=0){
                w*=md;
            }
            md=tab[i];
        }
        else{
            if(mu!=0){
                w*=mu;
            }
            mu=tab[i];
            x++;
        }
        w=((w%1000000007)+2000000014)%1000000007;

    }
    if(x%2){
        for(i=k; i<n; i++){
            if((tab[i]>0)&&(ikd==0)){
                ikd=tab[i];
            }
            if((tab[i]<0)&&(iku==0)){
                iku=tab[i];
            }
        }
        if(((md)&&(iku!=0))&&((mu)&&(ikd!=0))){
            mu=-mu;
            iku=-iku;
            if(mu*ikd>md*iku){
                w*=ikd;
                w=((w%1000000007)+2000000014)%1000000007;
                if(md!=0){
                    w*=md;
                }
                w=((w%1000000007)+2000000014)%1000000007;
            }
            else{
                w*=iku;
                w=((w%1000000007)+2000000014)%1000000007;
                if(mu!=0){
                    w*=mu;
                }
                w=((w%1000000007)+2000000014)%1000000007;
            }
        }
        else if((md)&&(iku!=0)){
            w*=iku;
            w=((w%1000000007)+2000000014)%1000000007;
            if(mu!=0){
                w*=mu;
            }
            w=((w%1000000007)+2000000014)%1000000007;
        }
        else if((mu)&&(ikd!=0)){
            w*=ikd;
            w=((w%1000000007)+2000000014)%1000000007;
            if(md!=0){
                w*=md;
            }
            w=((w%1000000007)+2000000014)%1000000007;
        }
        else{
            if(mu!=0){
                w*=mu;
            }
            w=((w%1000000007)+2000000014)%1000000007;
            if(md!=0){
                w*=md;
            }
            w=((w%1000000007)+2000000014)%1000000007;
        }
    }
    else{
        if(mu!=0){
            w*=mu;
        }
        w=((w%1000000007)+2000000014)%1000000007;
        if(md!=0){
            w*=md;
        }
        w=((w%1000000007)+2000000014)%1000000007;
    }
    if(id+iu<k){
        cout << "0\n";
        return 0;
    }
    if((id==0)&&(iu<n)){
        cout << "0\n";
        return 0;
    }
    cout << w << '\n';
    return 0;
}