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: Accepted)

n, k = map(int, input().split())
a = list(map(int, input().split()))
mod = 10 ** 9 + 7

plus = []
minus = []
for i in a:
    if i >= 0: plus.append(i)
    if i < 0: minus.append(-i)
plus.sort(reverse=True)
minus.sort(reverse=True)

ans = 1
if k == n:
    for x in a:
        ans = (ans * x) % mod
elif n == len(plus):
    for x in plus[:k]:
        ans = (ans * x) % mod
elif n == len(minus):
    if k % 2 == 1:
        ans = -1
        minus.sort()
    for x in minus[:k]:
        ans = (ans * x) % mod
else:
    i, j = 0, 0
    if k % 2 == 1:
        ans = plus[0]
        i += 1
    while i + j != k:
        x_p = plus[i] * plus[i + 1] if i < len(plus) - 1 else 0
        x_m = minus[j] * minus[j + 1] if j < len(minus) - 1 else 0
        if x_p > x_m:
            ans = (ans * x_p) % mod
            i += 2
        else:
            ans = (ans * x_m) % mod
            j += 2
print(ans)