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 8.8.3) (judge verdict: Accepted)

main = do
    [a,b,c,d] <- map read . words <$> getLine :: IO [Integer]
    let ab = b-a+1
    let c' = (div b c) - (div (a-1) c)
    let d' = (div b d) - (div (a-1) d)
    let cd' = (div b (lcm c d)) - (div (a-1) (lcm c d))
    print $ ab-(c'+d'-cd')