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)

# Bまで
bc = B/C
bd = B/D
blcm = B/lcm

ans_b = B - (bc+bd-blcm)

# Aまで
ac = (A-1)/C
ad = (A-1)/D
alcm = (A-1)/lcm

ans_a = (A-1) - (ac+ad-alcm)

# B - A
puts ans_b - ans_a