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 Ruby (2.7.1) (judge verdict: Runtime Error)

(N,K),A = $<.map{|ln| ln.split.map(&:to_i) }
M = 1000000007
A.sort_by!(&:abs)

if 0<K&1 && A.all?(&:negative?)
	prd = A.take(K).inject(1){|p,a| p*a%M }
	prd += M if prd<0
	p prd
	exit
end

k,prd,neg,nneg = K,1
while 1<k
	a = A.pop
	if a<0
		if neg
			prd,neg = a*neg*prd%M
			k -= 2
			if 0<k && nneg
				prd,nneg = nneg*prd%M
				k -= 1
			end
		else
			neg = a
		end
	else
		if nneg
			prd,nneg = nneg*prd%M,a
			k -= 1
		else
			nneg = a
		end
	end
end
prd = prd*(nneg||A.find{|a|0<=a})%M if 0<k
prd += M if prd<0
p prd