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 OCaml (4.02.3) (judge verdict: Accepted)

let a, b, c, d = Scanf.scanf " %d %d %d %d" @@ fun a b c d -> a, b, c, d
let rec gcd a b = if b = 0 then a else gcd b (a mod b)
let rec lcm a b = a / gcd a b * b
let f x = x / c + x / d - x / lcm c d
let _ = b - a + 1 - (f b - f (a - 1)) |> Printf.printf "%d\n"