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 (2.3.3) (judge verdict: Accepted)

a, b, c, d = gets.split.map(&:to_i)

b_cmod = b / c
b_dmod = b / d
b_cdmod = b / c.lcm(d)
bb = b_cmod + b_dmod - b_cdmod
# bt = b - b_cmod - b_dmod + b_cdmod

a_cmod = (a - 1) / c
a_dmod = (a - 1) / d
a_cdmod = (a - 1) / c.lcm(d)
aa = a_cmod + a_dmod - a_cdmod
# at = a - a_cmod - a_dmod + a_cdmod

# puts aa
# puts bb

# puts bt - at

puts b - a  + 1 - bb + aa

# puts b - a - bt + at