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: Runtime Error)

#include<bits/stdc++.h>
using namespace std;

#define mod 1000000007
using ll = long long;

int main(){

  int n,k;
  cin >> n >> k;

  //n==kの場合
  if(n==k){
    ll num;
    ll ans=1;
    for(int i=0;i<n;i++){
      cin >> num;
      ans=(ans*(num%mod))%mod;
    }
    cout << (ans+mod)%mod;
    return 0;
  }

  priority_queue<ll> pos;
  priority_queue<ll> neg;
  vector<ll> dp(k+1,1);
  ll num;
  for(int i=0;i<n;i++){
    cin >> num;
    if(num>=0){
      pos.push(num);
    }else{
      neg.push(-num);
    }
  }

  if(k%2==1 && pos.size()==0){
    ll ng;
    ll ans=1;
    for(int i=0;i<n;i++){
      ng=-neg.top();
      neg.pop();
      if(i>=n-k){
        ans=ans*ng%mod;
      }
    }
    cout << (ans+mod)%mod << endl;
    return 0;
  }

  ll posnum=1;
  ll negnum=1;
  bool posErase=1;
  bool negErase=1;
  ll ans=1;
  int i=0;
  if(k%2==1){
    posnum=pos.top();
    pos.pop();
    ans*=posnum;
    i++;
  }

  priority_queue<ll> que;
  while(pos.size()>=2){
    posnum=pos.top();
    pos.pop();
    posnum*=pos.top();
    pos.pop();
    que.push(posnum);
  }
  while(pos.size()>=2){
    negnum=neg.top();
    neg.pop();
    negnum*=neg.top();
    neg.pop();
    que.push(negnum);
  }
  for(int i=0;i<k/2;i++){
    ans*=que.top()%mod;
    que.pop();
  }

  cout << (ans+mod)%mod << endl;

}