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.lcm(d)

n_c = lcm / c
n_d = lcm / d
n = n_c + n_d - 1

q_a = a / lcm
q_b = b / lcm
r_a = a % lcm
r_b = b % lcm

a_to_lcm = unless r_a == 0 then n - ((r_a-1)/c + (r_a-1)/d) else n+1 end
lcm_to_b = r_b/c + r_b/d

division = a_to_lcm + (q_b - q_a - 1)*n + lcm_to_b

puts (b - a + 1) - division