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 split c s = (
    let res = ref [] in
    let i = ref 0 in
    let n = String.length s in
    while !i < n do
      let j = !i in
      while !i < n && s.[!i] <> c do i := !i + 1 done;
      res := String.sub s j (!i - j) :: !res;
      i := !i + 1;
    done;
    List.rev !res
  );;

let rec range a b = if a > b then [] else a :: range (a + 1) b;;
let read_ints () = read_line () |> split ' ' |> List.map int_of_string;;

let rec gcd x y = if y = 0 then x else gcd y (x mod y);;
let lcm x y = x / gcd x y * y;;

let [a; b; c; d] = read_ints ();;
let a = a - 1;;

let f x c d = x - x / c - x / d + x / lcm c d;;

print_int (f b c d - f a c d);;
print_newline ();;