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)

a,b,c,d = gets.chomp.split(' ').map(&:to_i)
c_a = (a-1)/c
d_a = (a-1)/d
c_b = b/c
d_b = b/d
lcm = c.lcm(d)
lcm_a = (a-1)/lcm
lcm_b = b/lcm
puts b - a + 1 - (c_b - c_a ) - (d_b - d_a) + (lcm_b - lcm_a)