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>
#define int long long
using namespace std;

bool cmp(int a, int b) {
    return abs(a) > abs(b);
}

const int MOD = 1e9 + 7;

signed main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    int n, k;
    cin >> n >> k;
    vector<int> a(n);
    for (int i = 0; i < n; i++) cin >> a[i];
    sort(a.begin(), a.end(), cmp);
    int afterpos = -1337, afterneg = 1337, insidepos = -1337, insideneg = 1337;
    int cntneg = 0, cntpos = 0;
    for (int i = 0; i < k; i++) {
        if (a[i] < 0) insideneg = a[i], cntneg++;
        else insidepos = a[i], cntpos++;
    }
    for (int i = n - 1; i >= k; i--) {
        if (a[i] < 0) afterneg = a[i];
        else afterpos = a[i];
    }
    int prod = 1;
    if (cntneg % 2 == 0) {
        for (int i = 0; i < k; i++) prod *= abs(a[i]), prod %= MOD;
        cout << prod;
        return 0;
    }
    else {
        int f = 0;
        if (afterpos == -1337 && insidepos == -1337) { /// If all are negative
            for (int i = n - k; i < n; i++) prod *= a[i] + MOD, prod %= MOD;
            cout << prod;
            return 0;
        }
        else if (afterpos == -1337 && afterneg != 1337 && insidepos != -1337) { /// If only pos -> neg
            for (int i = 0; i < k; i++) {
                if (!f && a[i] == insidepos) f = 1, prod *= abs(afterneg), prod %= MOD;
                else prod *= abs(a[i]), prod %= MOD;
            }
            cout << prod;
            return 0;
        }
        else if (insidepos == -1337 && insideneg != 1337 && afterpos != -1337) { /// If only neg -> pos
            for (int i = 0; i < k; i++) {
                if (!f && a[i] == insideneg) f = 1, prod *= abs(afterpos), prod %= MOD;
                else prod *= abs(a[i]), prod %= MOD;
            }
            cout << prod;
            return 0;
        }
        else if (afterneg != 1337 && insidepos != -1337 && insideneg != 1337 && afterpos != -1337) { /// If both possible
            int a1 = abs(insidepos * afterpos);
            int a2 = abs(insideneg * afterneg);
            if (a1 > a2) {
                for (int i = 0; i < k; i++) {
                    if (!f && a[i] == insideneg) f = 1, prod *= abs(afterpos), prod %= MOD;
                    else prod *= abs(a[i]), prod %= MOD;
                }
                cout << prod;
                return 0;
            }
            else {
                for (int i = 0; i < k; i++) {
                    if (!f && a[i] == insidepos) f = 1, prod *= abs(afterneg), prod %= MOD;
                    else prod *= abs(a[i]), prod %= MOD;
                }
                cout << prod;
                return 0;
            }
        }
    }
}