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)

def common_multiple(x, y):
    for i in range(2, min(x, y)+1):
        x0, y0 = x % i, y % i
        if x0 == 0 or y0 == 0:
            return common_multiple(x // i if x0 == 0 else x, y // i if y0 == 0 else y) * i
    return x * y

a = input().split(" ")
A, B, C, D = int(a[0]) - 1, int(a[1]), int(a[2]), int(a[3])

M = common_multiple(C, D)
B0 = B // C + B // D - B // M
A0 = A // C + A // D - A // M
print(B - A - B0 + A0)