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)

input = gets.chomp.split
a = input[0].to_i - 1
b = input[1].to_i
c = input[2].to_i
d = input[3].to_i

cd = c.lcm(d)

a_c = a / c
a_d = a / d
a_cd = a / cd

b_c = b / c
b_d = b / d
b_cd = b / cd

puts (b - b_c - b_d + b_cd) - (a - a_c - a_d + a_cd)