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 Control.Monad
import Data.Maybe
import Data.List
import qualified Data.ByteString.Char8 as BS
import qualified Data.Vector as V
 
main = abc161c

abc161c = do
    [n, k] <- getIntList
    let init = snd (divMod n k)
    let initV = V.fromList [init]
    print $ V.foldl' min n (operation initV init k)

operation :: V.Vector Integer -> Integer -> Integer -> V.Vector Integer
operation vec n k = let abs' = abs (n-k) in
    if V.elem abs' vec
        then vec
        else operation (V.cons abs' vec) abs' k

checkSelect :: Integer -> Integer -> Integer -> Bool
checkSelect m sum prod
    | prod * 4 * m < sum  = False
    | otherwise = True


readInt = fst . fromJust . BS.readInteger
readIntList = map readInt . BS.words
getIntList = readIntList <$> BS.getLine
getIntNList n = map readIntList <$> replicateM (fromIntegral n) BS.getLine