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 gcd(a, b):
    if a < b:
        a, b = b, a
    if b == 0:
        return a
    c = a % b
    return int(gcd(b, c))

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

A, B, C, D = list(map(int, input().split(" ")))

l = lcm(C, D)

A = A-1
x = (B-A)
y = (B//C - A//C)
z = (B//D - A//D)
a = (B//l - A//l)
print(x+a - (y+z))