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: Wrong Answer)

from fractions import gcd
Input = input()
a, b, c, d = Input.split()
a, b, c, d = int(a), int(b), int(c), int(d)
delta_c = (b-1)//c - a//c
delta_d = (b-1)//d - a//d
def lcm(x, y):
    return (x * y) // gcd(x, y)
cd = lcm(c, d)
delta_cd = (b-1)//cd - a//cd
num_cd = delta_c + delta_d - delta_cd
print( b-a+1 - num_cd, end='')