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<bits/stdc++.h>

using namespace std;
long M = 1e9 + 7, n, k, ans = 1, l, r, sign = 1, a[1 << 18], x, y, i;

main() {
    cin >> n >> k;
    for (i = 0; i < n; i++) cin >> a[i];
    sort(a, a + n);
    r = n - 1;

    if (k % 2 == 1) {
        ans = a[r], r--, k--;
        sign = (ans < 0 ? -1 : 1);
    }

    while (k) {
        x = a[l] * a[l + 1], y = a[r] * a[r - 1];
        if (x * sign > y * sign) ans *= x % M, ans %= M, l += 2;
        else ans *= y % M, ans %= M, r -= 2;
        k -= 2;
    }
    

    cout << (ans + M) % M << endl;
}