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 PyPy3 (7.3.0) (judge verdict: Accepted)

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

mia = sorted([i for i in a if i < 0], reverse=True)
pla = sorted([i for i in a if i >= 0])

cnt = 1
if len(pla) == 0 and k % 2 == 1:
    for i in mia[:k]:
        cnt = cnt * i % mod
    print(cnt)
    exit()

while k > 0:
    if k == 1 or len(mia) <= 1:
        if len(pla) == 0:
            cnt *= mia.pop()
        elif len(pla) > 0:
            cnt *= pla.pop()
        k -= 1
    elif len(pla) <= 1:
        cnt *= mia.pop() * mia.pop()
        k -= 2
    elif pla[-1] * pla[-2] > mia[-1] * mia[-2]:
        cnt *= pla.pop()
        k -= 1
    elif pla[-1] * pla[-2] <= mia[-1] * mia[-2]:
        cnt *= mia.pop() * mia.pop()
        k -= 2
    cnt %= mod
else:
    print(cnt)