Problem:
Score : 300 points

Problem Statement

Given any integer x, Aoki can do the operation below.

Operation: Replace x with the absolute difference of x and K.

You are given the initial value of an integer N. Find the minimum possible value taken by N after Aoki does the operation zero or more times.

Constraints

0 ≤ N ≤ 10^{18}

1 ≤ K ≤ 10^{18}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K

Output

Print the minimum possible value taken by N after Aoki does the operation zero or more times.

Sample Input 1

7 4

Sample Output 1

1

Initially, N=7.

After one operation, N becomes |7-4| = 3.

After two operations, N becomes |3-4| = 1, which is the minimum value taken by N.

Sample Input 2

2 6

Sample Output 2

2

N=2 after zero operations is the minimum.

Sample Input 3

1000000000000000000 1

Sample Output 3

0

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

import qualified Data.ByteString.Char8 as BS
import Data.Int (Int64)

main :: IO ()
main = do
  [x, y] <- map read . words <$> getLine :: IO [Int64]
  print $ solve x y


solve :: Int64 -> Int64 -> Int64
solve n k =
  let t = n `mod` k
  in
    min t (k - t)

iter :: Int64 -> Int64 -> Int64
iter n k = abs $ n - k


test :: IO ()
test = do
  print $ solve 7 4
  print $ solve 2 6
  print $ solve 1000000000000000000 1
  putStrLn "test finished"