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: Accepted)

#include <iostream>
#include <vector>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <algorithm>
#include <iomanip>
#include <numeric>
#include <queue>
#include <cmath>
using namespace std;

int main() {
    int n, k;
    cin >> n >> k;
    vector<long long int> vp, vn, vz;
    for (int i = 0; i < n; i++) {
        int t;
        cin >> t;
        if (t > 0) {
            vp.push_back(t);
        } else if (t < 0) {
            vn.push_back(t);
        } else {
            vz.push_back(t);
        }
    }
    if (vp.size() + vn.size() < k) {
        cout << 0 << endl;
        return 0;
    }
    int cn = vn.size(), cp = vp.size();
    long long int res = 1;
    const int mod = 1e9 + 7;
    bool flag;
    int kk = 0;
    kk += cn / 2 * 2;
    kk = min(kk, k / 2 * 2);
    if (kk + cp >= k) flag = true;
    else flag = false;

    if (!flag) {
        if (vz.size() > 0) {
            cout << 0 << endl;
            return 0;
        }
        for (int i = 0; i < vn.size(); i++) vn[i] *= -1;
        sort(vp.begin(), vp.end());
        sort(vn.begin(), vn.end());
        int i1 = 0, i2 = 1;
        if (k % 2 == 1) {
            res = vn[0];
            k -= 1;
        } else {
            res = vn[0] * vp[0] % mod;
            i1 = 1;
            k -= 2;
        }
        k /= 2;
        priority_queue<long long int, vector<long long int>, greater<long long int>> pq;
        for (int i = i1; i + 1 < vp.size(); i += 2) {
            pq.push(vp[i] * vp[i + 1]);
        }
        for (int i = i2; i + 1 < vn.size(); i += 2) {
            pq.push(vn[i] * vn[i + 1]);
        }
        for (int i = 0; i < k; i++) {
            res = res * (pq.top() % mod) % mod;
            pq.pop();
        }
        res %= mod;
        res *= -1;
        res = (res + mod) % mod;
        cout << res << endl;
        return 0;
    }
    priority_queue<long long int> pq;
    sort(vn.begin(), vn.end());
    for (int i = 0; i + 1 < cn; i += 2) {
        pq.push(vn[i] * vn[i + 1]);
    }
    sort(vp.begin(), vp.end(), greater<long long int>());
    for (int i = k % 2; i + 1 < cp; i += 2) {
        pq.push(vp[i] * vp[i + 1]);
    }
    if (k % 2 == 1) {
        res = vp[0];
    }
    k /= 2;
    for (int i = 0; i < k; i++) {
        res = res * (pq.top() % mod) % mod;
        pq.pop();
    }
    cout << res << endl;
}