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 PyPy3 (2.4.0) (judge verdict: Accepted)

def main():
    A, B, C, D = list(map(int, input().split()))
    candiv_C = num_can_div(A, B, C)
    candiv_D = num_can_div(A, B, D)
    candiv_lcm = num_can_div(A, B, lcm(C, D))

    print(B-A+1 - candiv_C - candiv_D + candiv_lcm)

def num_can_div(A, B, x):
    return B//x - (A-1)//x

def gcd(a, b):
    while b:
        a, b = b, a % b
    return a

def lcm(a, b):
    return a * b // gcd (a, b)

main()