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: Runtime Error)

from bisect import bisect_left

N,K = map(int,input().split())
a_list = list(map(int,input().split()))
a_list.sort()
b_list = a_list[-K:]

n_negative = bisect_left(a_list,0)

max_pair_num = min(n_negative//2, K//2)


# 負の数からiペア取る
n_product = 1
p_product = 1
for i in range(K):
    p_product*= b_list[i]

ans = p_product
for i in range(1,max_pair_num+1):
    n_product *= a_list[i*2-2]
    n_product *= a_list[i*2-1]

    p_product /= b_list[i*2-2]
    p_product /= b_list[i*2-1]

    if n_product*p_product>ans:
        ans = n_product*p_product

print(int(ans%1_000_000_007))