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: Wrong Answer)

n,k=map(int, input().split())
a = list(map(int, input().split()))
mod=10**9+7
if n==k:
    ans=1
    for i in range(k):
        ans*=a[i]
        ans%=mod
    print(ans)
    exit()

minus=[i for i in a if i<0]
plus=[i for i in a if i>=0]

minus=sorted(minus)
plus=sorted(plus,reverse=True)
if k%2==1 and len(plus)==0:
    ans=1
    for i in range(k):
        ans*=abs(minus[-i-1])
        ans%=mod
    print((mod-ans)%mod)
    exit()

n_minus=len(minus)
n_plus=len(plus)

m_saiyo=0
for i in range(0, n_minus+1, 2): # i個minusから採用
    if i==0:
        continue
    if 0<=k-i<n_plus-1 and (minus[i-1]*minus[i-2])>=(plus[k-i]*plus[k-i+1]):
        m_saiyo=i

ans=1

if set(plus)=={0}:
    if m_saiyo==0:
        print(0)
        exit()

for i in range(m_saiyo):
    ans*=minus[i]
    ans%=mod
for i in range(k-m_saiyo):
    try:
        ans*=plus[i]
    except:
        ans*=minus[-(i-n_plus)-1]
    ans%=mod

print(ans)