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;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int N, K;
    cin >> N >> K;
    vector<long long> A(N);
    for (int i = 0; i < N; ++i) {
        cin >> A[i];
    }
    sort(A.begin(), A.end(), [](long long i, long long j){
        return abs(i) >= abs(j);
    });
    int min_positive = -1, max_positive = -1, min_negative = -1, max_negative = -1;
    bool positive = true;
    for (int i = K - 1; i >= 0; --i) {
        if (A[i] < 0) {
            positive = !positive;
        }
        if (A[i] > 0 && min_positive == -1) {
            min_positive = i;
        } else if (A[i] < 0 && min_negative == -1) {
            min_negative = i;
        }
    }
    for (int i = K; i < N; ++i) {
        if (A[i] > 0 && max_positive == -1) {
            max_positive = i;
        } else if (A[i] < 0 && max_negative == -1) {
            max_negative = i;
        }
    }
    long long mod = 1E9 + 7;
    if (positive) {
        long long product = 1;
        for (int i = 0; i < K; ++i) {
            product = product * A[i] % mod;
        }
        cout << product << '\n';
        return 0;
    }
    bool pos2neg = (min_positive != -1 && max_negative != -1);
    bool neg2pos = (min_negative != -1 && max_positive != -1);
    if (!pos2neg && !neg2pos) {
        // all negative or 0
        long long product = 1;
        for (int i = N - 1; i >= N - K; --i) {
            product = product * A[i] % mod;
        }
        cout << (product + mod) % mod << '\n';
        return 0;
    }
    // choose min of A[min_positive] / A[max_negative], A[min_negative] / A[max_positive]
    if ((pos2neg && neg2pos && (A[min_positive] * A[max_positive] <= A[min_negative] * A[max_negative])) || pos2neg) {
        // pos -> neg
        long long product = 1;
        for (int i = 0; i < K; ++i) {
            if (i != min_positive) {
                product = product * A[i] % mod;
            }
        }
        product = product * A[max_negative] % mod;
        cout << product << '\n';
        return 0;
    } else {
        // neg -> pos
        long long product = 1;
        for (int i = 0; i < K; ++i) {
            if (i != min_negative) {
                product = product * A[i] % mod;
            }
        }
        product = product * A[max_positive] % mod;
        cout << product << '\n';
        return 0;
    }
    return 0;
}