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)

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

def gcd(x, y):
    while y != 0:
        (x, y) = (y, x % y)
    return x

betweenAandB = B-A+1

cA = (A-1)//C
cB = B//C
cDiv = cB - cA

dA = (A-1)//D
dB = B//D
dDiv = dB - dA

GCD = gcd(C,D)
LCM = C*D//GCD

lcmA = (A-1)//LCM
lcmB = B//LCM
lcmDiv = lcmB - lcmA

ans = betweenAandB - cDiv - dDiv + lcmDiv
print(ans)