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 Ruby (2.7.1) (judge verdict: Accepted)

data = $stdin.gets
a,b,c,d = data.split(" ").map{|x| x.to_i }
ab = b - a + 1
n_c = b/c - (a+c-1)/c + 1
n_d = b/d - (a+d-1)/d + 1
lcm_cd = c.lcm(d)
n_cd = b/lcm_cd - (a+lcm_cd-1)/lcm_cd + 1
result = (ab - n_c - n_d + n_cd)
puts result