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.chomp.split.map(&:to_i)

c_b = b/c
d_b = b/d
cd_b = b/(c*d/(c.gcd(d)))
c_a = (a-1)/c
d_a = (a-1)/d
cd_a = (a-1)/(c*d/(c.gcd(d)))


puts b - (c_b + d_b - cd_b)-(a-1 - (c_a + d_a - cd_a))