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)

n, k = map(int, input().split())
aa = list(map(int, input().split()))
import numpy as np
aa = np.array(aa)
mod = 10**9+7

def mul(dd):
    ret = 1
    for d in dd:
        ret = (ret*d)%mod
    return ret

def sol(aa, n, k):
    aap = aa[aa>0]
    aam = aa[aa<0]
    if n == k:
        return mul(aa)
    if len(aam) == n and k%2==1:
        aam.sort()
        aam = aam[::-1]
        return mul(aam[:k])

    aap.sort()
    aap = aap[::-1]
    aam.sort()

    ret=1
    if k%2 >0:
        k = k-1
        ret *= aap[0]
        aap = aap[1:]

    aap2 = [aap[2*i]*aap[2*i+1] for i in range(len(aap)//2)]
    aam2 = [aam[2*i]*aam[2*i+1] for i in range(len(aam)//2)]
    aap2.extend(aam2)
    aap2.sort(reverse=True)
    return (ret*mul(aap2[:k//2]))%mod

print(sol(aa, n, k))