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(x, y):
    """Greatest Common Divisor: O(min(x,y,))"""
    if y == 0:
        return x
    return gcd(y, x % y)


def lcm(x, y):
    """Lowest Common Multiple O(min(x,y,))"""
    return x * y // gcd(x, y)


def div_count(x, l, r):
    """Count Divisors"""
    return r // x - (l - 1) // x


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

# solve
div_cd = div_count(c, a, b) + div_count(d, a, b) - div_count(lcm(c, d), a, b)

print(b - a + 1 - div_cd)