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)


A,B,C,D=(int(x) for x in input().split(" "))
def gcd(x,y): 
  
   while(y): 
        x, y = y, x % y 
  
   return x 
def nb_divisers(n,m):
    return n//m
def nb_d_btw(f,g,n):
    if f%n==0:
        return nb_divisers(g,n)-nb_divisers(f,n)+1
    else:
        return nb_divisers(g,n)-nb_divisers(f,n)
def nb_notdivisers_f(a,b,c,d):
    e=int(c*d/gcd(c,d))
    return b-a+1-(nb_d_btw(a,b,c)+nb_d_btw(a,b,d)-nb_d_btw(a,b,e))
print(nb_notdivisers_f(A,B,C,D))