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 = do 
    [a, b, c, d] <- map (read :: String -> Integer). words <$> getLine

    let d1 = div (a-1) c
    let d2 = div (a-1) d
    let d3 = div (a-1) (lcm c d)
    let d4 = div b c
    let d5 = div b d
    let d6 = div b (lcm c d)

    print $ b - a + 1 - ((d4 + d5 - d6) - (d1 + d2 - d3))