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;
using  ll = long long;
#define rep(i,n) for (int i = 0; i < (n); ++i)
using P=pair<ll,bool>;

const ll MOD=1e9+7;

int main(){
  ll n,k;
  std::cin >> n >>k;
  std::vector<P> a;

  ll pcnt=0;
  rep(i,n){
    ll temp;
    std::cin >> temp;
    if(temp>0){a.push_back(P(temp,true));pcnt++;}
    else if(temp<0){a.push_back(P(-temp,false));}
  }

  if(a.size()<k){
    std::cout << "0" << '\n';
    return 0;
  }

  ll ans=1;

  if(pcnt>=k){
    sort(a.rbegin(),a.rend());
    ll stock=0;
    bool sch=false;
    ll nk=0;
    rep(i,n){
      if(a[i].second){
        ans*=a[i].first;
        ans%=MOD;
        nk++;
      }
      else {
        if(sch&&nk+2<=k){
          ans*=stock;
          ans%=MOD;
          ans*=a[i].first;
          ans%=MOD;
          
          sch=false;
          nk+=2;
        }else{
          stock=a[i].first;
          sch=true;
        }
      }
      if(nk==k)break;
    }

  }else{
    sort(a.begin(),a.end());
    rep(i,k){
      ans*=a[i].first;
      ans%=MOD;
    }
    ans*=-1;
    ans%=MOD;
    if(ans<0)ans+=MOD;

  }






  std::cout << ans << '\n';


  return 0;
}