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 = map(int, input().split())
if a % c == 0:
    div_c = b//c - a//c +1
else:
    div_c = b//c - a//c 
if a % d == 0:
    div_d = b//d - a//d + 1
else:
    div_d = b//d - a//d
x = c*d // gcd(c,d)
if a % x == 0:
    div_cd = b//x - a//x + 1
else:
    div_cd = b//x - a//x
print(b-a+1 - div_c -div_d + div_cd)