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)

lcm = [c, d].inject{|a,b| a.lcm(b)}
c_divisors = (b / c) - ((a - 1) / c)
d_divisors = (b / d) - ((a - 1) / d)
common_divisors = (b / lcm) - ((a - 1) / lcm)
cd_divisors = c_divisors + d_divisors - common_divisors

ans = b - a + 1 - cd_divisors

puts ans