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)

can_devide_c = b / c - (a - 1)/ c
can_devide_d = b / d - (a - 1)/ d
can_devide_c_and_d = b / c.lcm(d) - (a - 1) / c.lcm(d)
can_devide_c_or_d = can_devide_c + can_devide_d - can_devide_c_and_d
count = b - a + 1 - can_devide_c_or_d

puts count