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;

int main()
{
    int n, m, i;
    long long int res=1, tempInt, mod=1e9+7;
    cin>>n>>m;
    vector<long long int> pos;
    vector<long long int> neg;
    for(i=0;i<n;i++)
    {
        cin>>tempInt;
        if(tempInt<0)
            neg.push_back(tempInt);
        else
            pos.push_back(tempInt);
    }
    if(m==n)
    {
        for(i=0;i<pos.size();i++)
            res=(res*pos[i])%mod;
        for(i=0;i<neg.size();i++)
            res=(res*neg[i])%mod;
        if(res<0)
            res+=mod;
        cout<<res<<endl;
        return 0;
    }
    if(neg.empty())
    {
        sort(pos.rbegin(),pos.rend());
        for(i=0;i<m;i++)
            res=(res*pos[i])%mod;
        cout<<res<<endl;
        return 0;
    }
    sort(neg.begin(),neg.end());
    //cout<<"Neg Sorted\n";
    if(pos.empty())
    {
        if( m%2)
        {
            for(i=neg.size()-1;i>=neg.size()-m;i--)
                res=(res*neg[i])%mod;
            cout<<mod+res<<endl;
            return 0;
        }
        else
        {
            for(i=0;i<m;i++)
                res=(res*neg[i])%mod;
            cout<<res<<endl;
            return 0;
        }

    }
    sort(pos.rbegin(),pos.rend());
    //cout<<"Pos Sorted\n";
    int j,k;
    i=0;
    j=0;
    k=0;
    while(i<m)
    {
        //cout<<"Choosing "<<i+1<<"\n";
        if(i==m-1  || k>neg.size()-2)
        {
            res=(res*pos[j])%mod;
            //cout<<"Chose: pos["<<j<<"]: "<<pos[j]<<endl;
            j++;
            i++;
        }
        else
        {
            if( j==pos.size()-1 )
            {
                res=(res*(neg[k]*neg[k+1])%mod)%mod;
                //cout<<"Chose: neg["<<k<<"]: "<<neg[k]<<"& neg["<<k+1<<"]: "<<neg[k+1]<<endl;
                k+=2;
                i+=2;
            }
            else if(pos[j]*pos[j+1]>neg[k]*neg[k+1])
            {
                res=(res*pos[j])%mod;
                //cout<<"Chose: pos["<<j<<"]: "<<pos[j]<<endl;
                j++;
                i++;
            }
            else
            {
                res=(res*(neg[k]*neg[k+1])%mod)%mod;
                //cout<<"Chose: neg["<<k<<"]: "<<neg[k]<<"& neg["<<k+1<<"]: "<<neg[k+1]<<endl;
                k+=2;
                i+=2;
            }
        }
    }

    cout<<res<<endl;
    return 0;
}