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 Python (3.8.2) (judge verdict: Wrong Answer)

import math
A, B, C, D = map(int, input().split())
 
# CでもDでも割り切れない = 全体(a) - Cで割り切れる(b) + Dで割り切れる(c) + CでもDでも割り切れる(d)
lcm = C*D // math.gcd(C, D)
a = B-A+1

if A % C != 0 and B % C != 0: b = a // C
else: b = a // C + 1
if A % D != 0 and B % D != 0: c = a // D
else: c = a // D + 1
if A % lcm != 0 and B % lcm != 0: d = a // lcm
else: d = a // lcm + 1

print(a-b-c+d)