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 () =
    let rec gcd a b = if b = 0 then a else gcd b (a mod b) in
    let lcm a b = let g = gcd a b in a / g * b in
    let calc a c d =
        let divisible_by_c = a / c in
        let divisible_by_d = a / d in
        let divisible_by_c_and_d = a / lcm c d in
        a - divisible_by_c - divisible_by_d + divisible_by_c_and_d
    in
    let main () =
        let a, b, c, d = Scanf.sscanf (read_line ()) "%d %d %d %d" (fun a b c d -> a, b, c, d) in
        let s = calc b c d - calc (a - 1) c d in
        Printf.printf "%d\n" s
    in
    main ()