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 (2.7.1) (judge verdict: Accepted)

a, b, c, d = gets.split.map(&:to_i)

cnt = 0
min_c = a % c == 0 ? (a / c) : (a / c + 1)
max_c = b / c

c_cnt = max_c - min_c + 1

min_d = a % d == 0 ? (a / d) : (a / d + 1)
max_d = b / d

d_cnt = max_d - min_d + 1

cd_lcm = c.lcm(d)

min_cd = a % d == 0 ? (a / cd_lcm) : (a / cd_lcm + 1)
max_cd = b / cd_lcm 

cd_cnt = max_cd - min_cd + 1

puts (b - a + 1 - (c_cnt + d_cnt - cd_cnt))