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 Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

;m以上n以下でNの倍数の個数を数える
(defun count-m (m n k)
  (-(floor n k)
    (floor (1- m) k)))

(defun solve (A B C D)
  (let  (( E (lcm C D)))
    (- (1+ (- B A))
       (- (+ (count-m A B C)
	     (count-m A B D))
	  (count-m A B E)))))

(princ (solve (read) (read) (read) (read)))