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)

# ABC 131 anti division

a, b, c, d = [int(el) for el in input().split(' ')]

def gcd(x, y):
    while(y):
        x, y = y, x % y
    return x

def lcm(x, y):
    return(x*y // gcd(x, y))

def g(x, y):
    return(x // y + 1)

def f(x, y, z):
    return(x+1 - g(x, y) - g(x, z) + g(x, lcm(y, z)))

print(f(b, c, d) - f(a-1, c, d))