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;

#define int long long
#define endl "\n"
#define mod 1000000007
#define pb push_back
#define ff first
#define ss second
#define FIO ios_base::sync_with_stdio(false); cin.tie(NULL);


main(){
	FIO
	int n,k;
	cin>>n>>k;
	int i,j,pos=0;
	vector<pair<int,int>>vec;
	for(i=0;i<n;i++){
		cin>>j;
		if(j>=0){
			pos++;
			vec.pb({abs(j),1});
		}
		else{
			vec.pb({abs(j),0});
		}
		
	}
		sort(vec.begin(),vec.end());
		int pro=1;
		//cout<<pos<<endl;
		if(pos<k){
			for(i=0;i<k;i++){
				if(vec[i].ss==0){
					pro = pro*vec[i].ff*(-1);
					pro = (pro%mod + mod)%mod;
				}
				else{
					pro = pro*vec[i].ff;
					pro = (pro%mod + mod)%mod;
				}
			}
			cout<<pro<<endl;
		}
		else{
			int neg=0,l=k;j=0;
			for(i=n-1;k>0;i--){
				k--;
				if(vec[i].ss==0){
					j++;
				}
			}
			
			k = l;
			if(j%2==0){
				for(i=n-1;k>0;i--){
					k--;
					if(vec[i].ss==0){
						pro = pro*vec[i].ff*(-1);
						pro = (pro%mod + mod)%mod;
					}
					else{
						pro = pro*vec[i].ff;
						pro = (pro%mod + mod)%mod;
					}
				}
				cout<<pro<<endl;
			}
			else{
				//cout<<j<<endl;
				for(i=n-1;k>0;i--){
					if(vec[i].ss==0){
						if(neg<j-1){
							//cout<<"neg"<<endl;
							pro = pro*vec[i].ff*(-1);
							pro = (pro%mod + mod)%mod;
							neg++;
							k--;	
						}
					}
					else{
						// cout<<"pos"<<endl;
						// cout<<pro<<endl;
						pro = pro*vec[i].ff;
						pro = (pro%mod + mod)%mod;
						k--;
					}
				}
				cout<<pro<<endl;
			}
		
	}
}