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<cmath>
#include<algorithm>
#include<string>
#include<queue>
using namespace std;
#define ll long long
int n,k;
vector<ll> pos,neg,res;
ll ans=1,cons=1000000007;

signed main(){
	cin>>n>>k;
	for(int i=0;i<n;i++){
	   ll v;cin>>v;
	   if(v>=0){pos.push_back(v);
	   }
	   else neg.push_back(v*(-1));
	   ans*=v;
	   ans%=cons;
	}
	if(k==n){cout<<(ans)%cons<<endl; return 0;
	}
	ans=1;
	sort(neg.begin(),neg.end());
	sort(pos.begin(),pos.end());
	if(pos.empty()){
		ans=1;
		if(k%2){
			for(int i=0;i<k;i++)ans=(ans*neg[i])%cons;
			ans*=-1;
		}
		else{
			for(int i=neg.size()-1;i>=neg.size()-k;i--){
				ans=(ans*neg[i])%cons;
			}
		}
		cout<<(ans+cons)%cons;return 0;
	}
	else{
		if(k%2==1){
		    res.push_back(pos.back());
		    pos.pop_back();
		}
		while(res.size()<k){
			bool ppos=0,pneg=0;ll pos1,neg1,pos2,neg2;
			if(pos.size()>=2){ppos=1;pos1=pos.back();
			pos2=pos[pos.size()-2];
			}
			if(neg.size()>=2){pneg=1;neg1=neg.back();
			neg2=neg[neg.size()-2];
			}
			if(ppos&&pneg){
				if(pos1*pos2>neg1*neg2){
					pos.pop_back();
					pos.pop_back();
					res.push_back(pos1);res.push_back(pos2);
				}
				else{
					neg.pop_back();neg.pop_back();
					res.push_back(neg1);res.push_back(neg2);
				}
			}
			if(pneg&&!ppos){
				neg.pop_back();neg.pop_back();
					res.push_back(neg1);res.push_back(neg2);
			}
			if(ppos&&!pneg){
				pos.pop_back();
					pos.pop_back();
					res.push_back(pos1);res.push_back(pos2);
			}
			if(!ppos&&!pneg){
				res.push_back(pos.back());pos.pop_back();
				res.push_back(neg.back());neg.pop_back();
			}		
	}
	}
	for(int i=0;i<k;i++)ans=(ans*res[i])%cons;
	cout<<ans<<endl;
	return 0;
}