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: Runtime Error)

from functools import reduce
import numpy as np

mod=10**9+7

def mat(list):
    return reduce(lambda a,b: a*b%mod, list)


N, K = list(map(int, input().split()))
A = list(map(int, input().split()))
A = np.array(sorted(A, key=abs, reverse=True))
A_pn = A < 0
print(A_pn)
if N == np.count_nonzero(A_pn):
    if K % 2 == 0:
        print(mat(A[:K]))
    else:
        print(mat(A[-K:]))
elif np.count_nonzero(A_pn[:K]) % 2 == 0:
    print(mat(A[:K]))
else:
    for a in A[K:]:
        if a >= 0:
            last = a
    print(mat(A[:K-1])*last)