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: Time Limit Exceeded)

a, b, c, d = gets.chomp.split(" ").map(&:to_i)
result = 0
c_c = c
d_d = d
while c_c <= b || d_d <= b
  if c_c >= a && c_c <= b
    result += 1
  end
  if d_d >= a && d_d <= b
    result += 1
  end
  c_c += c
  d_d += d
end

min = c.lcm(d)
min_m = min
while min_m <= b
  if min_m >= a
    result -= 1
  end
  min_m += min
end

puts ((b - a + 1) - result)