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 rep(i, n) for (int i = 0; i < (int)(n); i++)
using ll = long long;
using vi = vector<int>;
using vvi = vector<vi>;
using vl = vector<ll>;
using vvl = vector<vl>;

int main(){
  ll MOD = 1000000007;
  int n, k;
  cin >> n >> k;
  vl pos, neg;
  int cntp=0, cntn=0;
  rep(i,n){
    int a;
    cin >> a;
    if(a > 0){
      pos.push_back(a);
      cntp++;
    }
    else if(a < 0){
      a *= -1;
      neg.push_back(a);
      cntn++;
    }
  }
  if(cntn == 0) neg.push_back(0);
  if(cntp == 0) pos.push_back(0);
  sort(pos.rbegin(),pos.rend());
  sort(neg.rbegin(),neg.rend());
  ll ans = 1;
  int po = 0, ne = 0;
  
  if(cntp == 0 && k%2 == 1){
    vl v(n);
    rep(i,cntp) v[i] = pos[i];
    rep(i,cntn) v[i+cntp] = neg[i];
    sort(v.begin(),v.end());
    rep(i,k){
      ans *= v[i];
      ans %= MOD;
    }
    ans *= -1;
    ans += MOD;
  }
  
  else {
    rep(i,k){
      if(pos[po] > neg[ne] * neg[ne+1] && po < cntp && ne + 1 < cntn){
        ans *= pos[po];
        po++;
      }
      else if(pos[po] * pos[po+1] > neg[ne] * neg[ne+1] && po + 1 < cntp && ne + 1 < cntn){
        ans *= pos[po] * pos[po+1];
        i++;
        po += 2;
      }
      else if(pos[po] * pos[po+1] <= neg[ne] * neg[ne+1] && po + 1 < cntp && ne + 1 < cntn){
        ans *= neg[ne] * neg[ne+1];
        i++;
        ne += 2;
      }
      else if(po < cntp){
        ans *= pos[po];
        po++;
      }
      else{
        ans *= neg[ne];
        ne++;
      }
      ans %= MOD;
    }
  }
  
  cout << ans << endl;
}