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: Accepted)

MOD = 10**9 + 7
pos = []
neg = []
n, k = gets.split.map(&:to_i)
gets.split.map(&:to_i).each{|a|
	if a >= 0
		pos.push(a)
	else
		neg.push(-a)
	end
}
pos.sort!
neg.sort!

ans = 1
if ([neg.size, k].min & ~1) + pos.size >= k
	if k % 2 == 1
		ans = ans * pos.pop % MOD
		k -= 1
	end
	while k > 0
		if neg.size < 2 || (pos.size >= 2 && pos[-1] * pos[-2] > neg[-1] * neg[-2])
			ans = ans * pos.pop % MOD * pos.pop % MOD
		else
			ans = ans * neg.pop % MOD * neg.pop % MOD
		end
		k -= 2
	end
else
	ans = MOD - 1
	[*pos, *neg].min(k).each{|x| ans = ans * x % MOD }
end

puts ans