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: Wrong Answer)

def prod(llst):
	P=1
	if len(llst)==0:
		p=P*0
	else:
		for i in llst:
			P=P*i
	return P
n,k=map(int,input().split())
lst=list(map(int,input().split()))
lst.sort(reverse=True)
maxlst=[]
i=0
while i<n:
	if lst[i]<0:
		break
	maxlst.append(lst[i])
	i=i+1
minlst=lst[i:]
#minlst.sort(reverse=True)
#maxlst.sort(reverse=True)
#print(minlst,maxlst)
maxp=prod(maxlst[:k])
mp=prod(minlst[:k])
if k%2==0:
	if mp>maxp:
		print(mp%1000000007)
	else:
		print(maxp%1000000007)
else:
	if len(maxlst)==0:
		print(mp%1000000007)
	else:
		print(maxp%1000000007)