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)

main :: IO ()
main = do
  [a,b,c,d] <- map (read :: String -> Int) . words <$> getLine
  print $ (ans b c d) - (ans (a-1) c d)

ans :: Int -> Int -> Int -> Int
ans n c d = n - div n c - div n d + div n (lcm c d)