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 (3.4.3) (judge verdict: Accepted)

def getDivisableCount(min_bound, max_bound, div):
    return max_bound // div - (min_bound - 1) // div

def LCM(a, b):
    return a * b // GCD(a, b)

def GCD(a, b):
    if a > b:
        a, b = b, a
    while b % a != 0:
        a, b = b % a, a
    return a

if __name__ == '__main__':
    A, B, C, D = [int(i) for i in input().split()]
    ret = (B - A + 1) - getDivisableCount(A, B, C) - getDivisableCount(A, B, D) + getDivisableCount(A, B, LCM(C, D))
    print(ret)