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 Haskell (GHC 8.8.3) (judge verdict: Time Limit Exceeded)

import qualified Data.ByteString.Char8 as BS
import Data.Char
import Data.List

main = do
  li <- BS.getLine
  let [n,k] = unfoldr (BS.readInt . BS.dropWhile isSpace) li
  li <- BS.getLine
  let as = unfoldr (BS.readInt . BS.dropWhile isSpace) li
  let ans = compute n k as
  print ans

base = 10^9+7

compute :: Int -> Int -> [Int] -> Integer
compute n k as = flip mod base $ maximum $ zipWith (*) pprods1 (reverse mprods1)
  where
    as1 = map fromIntegral $ sort as
    as2 = reverse as1
    pprods = scanl (*) 1 as2
    mprods = scanl (*) 1 as1
    k1 = succ k
    pprods1 = take k1 (pprods ++ repeat 1)
    mprods1 = take k1 (mprods ++ repeat 1)