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)

A, B, C, D = map(int, input().split())

def multiple(X, Y, Z):
    min_z = X // Z + 1
    max_z = Y // Z 
    num_z = max_z - min_z + 1
    return num_z 

def gcd(X, Y):
    while Y!= 0:
        X, Y = Y, X % Y
    return X

if C == 1 or D == 1:
    print(0)
else:
    num_c = multiple(A, B, C)
    print(num_c)
    num_d = multiple(A, B, D)
    print(num_d)
    lcm = int((C * D) / gcd(C, D)) 
    num_lcm = multiple(A, B, lcm)
    print(B - A + 1 - num_c - num_d + num_lcm)