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 Control.Applicative
import Control.Monad
import Data.List

main = do
  [a, b, c, d] <- map (read::String -> Integer) . words <$> getLine
  let gcd = calcGcd c d
      lcm = (c * d) `div` gcd
      a_num = (a - 1) `div` c + (a - 1) `div` d - (a - 1) `div` lcm
      b_num = b `div` c + b `div` d - b `div` lcm
  print $ b - a + 1 - b_num + a_num

calcGcd::Integer -> Integer -> Integer
calcGcd x y
 | x < y = calcGcd y x
 | x `mod` y == 0 = y
 | otherwise = calcGcd y (x `mod` y)