Problem:
Score : 300 points

Problem Statement

You are given four integers A, B, C, and D. Find the number of integers between A and B (inclusive) that can be evenly divided by neither C nor D.

Constraints

1\leq A\leq B\leq 10^{18}

1\leq C,D\leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B C D

Output

Print the number of integers between A and B (inclusive) that can be evenly divided by neither C nor D.

Sample Input 1

4 9 2 3

Sample Output 1

2

5 and 7 satisfy the condition.

Sample Input 2

10 40 6 8

Sample Output 2

23

Sample Input 3

314159265358979323 846264338327950288 419716939 937510582

Sample Output 3

532105071133627368

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

import Data.Bits
import Data.List
import Control.Monad
import qualified Data.Vector.Unboxed as V
import Control.Monad.ST

main :: IO ()
main = do
  [a,b,c,d] <- map read.words <$> getLine :: IO [Int]
  let f x = if a `mod` x == 0 then (+1) $ (b - a) `div` x else (+1) $ ( b - ((*x) $ (a `div` x) + 1)) `div` x
  putStrLn $ show $ b - a + 1 - ((f c) + (f d) - (f $ lcm d c))