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)

import math
A, B, C, D = map(int, input().split())
U = B - A + 1

MofD = 0
MofCD = 0

def gcd(x, y):
    if y == 0:
        return x
    else:
        return gcd(y, x % y)

def lcm(x, y):
    return (x * y) // gcd(x, y)


def sten(st, en, x):
    st = math.ceil(st/x)*x
    en = math.floor(en/x)*x
    if en >= st:
        n = (en - st) // x + 1
    else:
        n = 0
    return n


MofC = sten(A, B, C)
if C != D:
    MofD = sten(A, B, D)
    MofCD = sten(A, B, lcm(C, D))

print(U-MofC-MofD+MofCD)