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 2.0.3) (judge verdict: Accepted)

(defun div-num (a b x)
  (multiple-value-bind (n m) (floor (/ (+ (- b a) 1) x))
    (cond ((= m 0)
           n)
          ((= (mod a x) 0)
           (1+ n))
          ((> (mod a x) (mod b x))
           (1+ n))
          (t n))))
(let ((a (read))
      (b (read))
      (c (read))
      (d (read)))
  (format t "~A~%" (- (+ (div-num a b 1) (div-num a b (lcm c d)))
                      (+ (div-num a b c) (div-num a b d)))))