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)

from fractions import gcd


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


def counter(n, a):
    return n // a


a, b, c, d = map(int, input().split())
l = lcm(c, d)
print(b - a + 1 - (counter(b, c) - counter(a - 1, c) +
                   counter(b, d) - counter(a - 1, d) -
                   (counter(b, l) - counter(a - 1, l))))