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           Control.Monad.ST
import qualified Data.Array                  as A
import qualified Data.Array.ST               as ST
import qualified Data.Array.Unboxed          as AU
import           Data.Bits
import qualified Data.ByteString.Char8       as BS
import           Data.Char
import           Data.Int
import qualified Data.IntMap                 as IM
import           Data.List
import qualified Data.Map                    as M
import           Data.Maybe
import           Data.Ord
import qualified Data.Set                    as S
import           Data.Time
import qualified Data.Vector                 as V
import qualified Data.Vector.Mutable         as VM
import qualified Data.Vector.Unboxed         as VU
import qualified Data.Vector.Unboxed.Mutable as VUM

readInt :: IO [Int]
readInt = map (fst . fromJust . BS.readInt) . BS.words <$> BS.getLine

readInts :: Int -> IO [[Int]]
readInts n = replicateM n readInt

readInteger :: IO [Integer]
readInteger = map (fst . fromJust . BS.readInteger) . BS.words <$> BS.getLine

readIntegers :: Int -> IO [[Integer]]
readIntegers n = replicateM n readInteger

readString :: IO [String]
readString = map BS.unpack . BS.words <$> BS.getLine

readStrings :: Int -> IO [[String]]
readStrings n = replicateM n <$> readString

toPair :: [a] -> (a, a)
toPair [x, y] = (x, y)

count :: Eq a => a -> [a] -> Int
count a as = length $ filter (== a) as

main = do
  [n, k] <- readInt
  let (a, b) = n `divMod` k
   in print $ min b (k - b)