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)

D = 10**9+7
N,K,*A = $<.read.split.map &:to_i
A.sort!
i = A.bsearch_index {0 <= _1} || N
M = A[0...i]
j = A[i...N].bsearch_index {0 < _1} || N-i
Z = A[i,j]
P = A[i+j...N]
A.sort_by! {|a| a<0 ? -1-a-a : a+a }
A.shift j
m = (K > P.size + M.size/2*2) ? 1 : (K.odd? && !P[0])
exit p(0)  if m && j>0
if m
  s = 1
  A[0,K].each{s *= _1; s %= D if s > D }
  p (s+D) % D
  exit
end  
k,s = K,1
a,b = P.pop 2
c,d = M.shift 2
while k > 1 && b && d
  k -= 2
  if (x=a*b) > (y=c*d)
    s = s*x % D
    a,b = P.pop 2
  else
    s = s*y % D
    c,d = M.shift 2
  end
end
(s = c*d*s % D; c,d = M.shift 2; k-=2)  while d && k > 1
(s *= b; k-=1)  if b && k > 0
(s = s*a % D; a = P.pop; k-=1)  while k > 0
p s % D