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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

from math import log
mod = int(1e9) + 7
n, k = [int(i) for i in input().split()]
a = [int(i) for i in input().split()]
a.sort()
m, ok = 0, 0

def sign(v):
    if v == 0:
        return 0
    return 1 if v > 0 else -1

for i in range(k + 1):
    c = 1
    sm = 0
    sgn = 1
    for j in range(i):
        c = c * a[j] % mod
        sgn *= sign(a[j])
        if a[j] != 0:
            sm += log(abs(a[j]))
    for j in range(k - i):
        c = c * a[n - j - 1] % mod
        sgn *= sign(a[n - j - 1])
        if a[n - j - 1] != 0:
            sm += log(abs(a[n - j - 1]))
    if not ok:
        m = (sgn * sm, c)
        ok = 1
    else:
        m = max(m, (sgn * sm, c))
    
print(m[1])