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: Time Limit Exceeded)

#include<bits/stdc++.h>
using namespace std;
#define MOD 1000000007
long long product(long long *arr,long long n,long long k)
{ 
  if(k==0)
    return 1;
  if(n==0)
    return 0;
  long long o1=((arr[0]%MOD)*(product(arr+1,n-1,k-1)%MOD))%MOD;
  long long o2=(product(arr+1,n-1,k)%MOD);
  //cout<<o1<<" "<<o2<<endl;
 if(o1==0)
   return o2%MOD;
  if(o2==0)
    return o1%MOD;
  return max(o1,o2);
}
int main()
{
  long long n,k;
  cin>>n>>k;
  long long *arr=new long long[n];
  for(long long i=0;i<n;i++)
    cin>>arr[i];
  long long ans=product(arr,n,k);
  if(ans!=-12)
  cout<<(ans+MOD)%MOD<<endl;
  else
  {
    cout<<1000000001<<endl;
  }
  
}