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: Accepted)

import math
A, B, C, D = map(int, input().split())

c = (B//C) - ((A+C-1)//C) + 1
d = (B//D) - ((A+D-1)//D) + 1
lcm = int(C * D / math.gcd(C, D))
m = (B//lcm) - ((A+lcm-1)//lcm) + 1
ans = (B-A+1) - (c+d-m)
print(int(ans))