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 math import ceil

def gcd(m,n):
    x=max(m,n)
    y=min(m,n)
    if x%y == 0:
        return y
    else:
        while x%y != 0:
            z = x%y
            x = y
            y = z
        else:
            return z

def lcm(m,n):
    return int(m*n/gcd(m,n))

A,B,C,D=map(int,input().split())
__C = ceil((B-A)/C)
__D = ceil((B-A)/D)
min_mul = lcm(C,D)
B__CD = ceil(B//min_mul)
A__CD = ceil(A//min_mul)
C__D = B__CD - A__CD
print( (B-A+1) - (__C+__D) + C__D )