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
a.sort()

if n==k:
    ans=1
    for num in a:
        ans*=num
        ans%=mod
    print(ans)
    exit()

if a[-1]<0: # all a is minus
    if k%2==1: # ans is minus
        a.sort(reverse=True)
        ans=1
        for num in a[:k]:
            ans*=num
            ans%=mod
        print(ans)
        exit()

# ans>=0

ans=1
if k%2==1:
    ans=a[-1]
    a.pop(-1)
    k-=1

pz_a=[]
m_a=[]

for num in a:
    if num<0:
        m_a.append(num)
    else:
        pz_a.append(num)
pz_a.sort(reverse=True)

c2_a=[]
lastnum=-1
for i in range(len(pz_a)):
    num1=pz_a[i]
    if lastnum==-1:
        lastnum=num1
    else:
        c2_a.append(lastnum*num1)
        lastnum=-1

lastnum=1
for i in range(len(m_a)):
    num1=m_a[i]
    if lastnum==1:
        lastnum=num1
    else:
        c2_a.append(lastnum*num1)
        lastnum=1

c2_a.sort(reverse=True)

for num in c2_a[:k//2]:
    ans*=num
    ans%=mod

print(ans)