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)

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

def gcd(p, q):
    if q > p:
        p, q = q, p
    m = -1
    while m != 0:
        m = p % q
        p, q = q, m
    return p

a = a - 1
lcm = c * d // gcd(d, c)
dc = b//c - a//c
dd = b//d - a//d
dcd = b//lcm - a//lcm
divable = dc + dd - dcd
print(b - a - divable)