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)

def gcd(a, b)
  a, b = b, a if a < b
  return a if b == 0
  _mod = a.modulo(b)
  if _mod == 0
    b
  else
    gcd(b, _mod)
  end
end

def lcm(a, b)
  a * b / gcd(a, b)
end


# A以下のCの約数の個数
A_1 = A - 1

a_c_cnt = A_1/C
a_d_cnt = A_1/D
a_cd_cnt = A_1/lcm(C,D)

a_cnt = A_1 - a_c_cnt - a_d_cnt + a_cd_cnt

b_c_cnt = B/C
b_d_cnt = B/D
b_cd_cnt = B/lcm(C,D)

b_cnt = B - b_c_cnt - b_d_cnt + b_cd_cnt


p b_cnt - a_cnt