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: Wrong Answer)

{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE BinaryLiterals #-}
{-# LANGUAGE MultiWayIf #-}
{-# LANGUAGE NumDecimals #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TupleSections #-}

import Control.Applicative
import Control.Arrow
import Control.Monad
import Control.Monad.ST

import Data.Char
import Data.List
import Data.Maybe

import qualified Data.ByteString.Char8 as B

import Data.Array.ST.Safe
import Data.STRef

import Debug.Trace
import Text.Printf

readInt = readLn :: IO Int
readInteger = readLn :: IO Integer
readInts = map ( fst . fromJust . B.readInt ) . B.words <$> B.getLine
readIntegers = map ( fst . fromJust . B.readInteger ) . B.words <$> B.getLine

which a b f = if f then a else b
mp [ a, b ] = ( a, b )

modifyArray a i f = writeArray a i =<< f <$> readArray a i

main = readIntegers >>= print . uncurry mod . mp