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
a,b,c,d = (int(x) for x in input().split())
val = gcd(c,d)
lcm = (c*d) // val
div_by_c = (b // c) - (a // c) + (1 if a % c == 0 else 0)
div_by_d = (b // d) - (a // d) + (1 if a % d == 0 else 0)
div_by_lcm = (b // lcm) - (a // lcm) + (1 if a % lcm == 0 else 0)

print(b-a+1 - div_by_c - div_by_d + div_by_lcm)