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 fractions
A, B, C, D = map(int, input().split())
Cdiv = B // C - (A - 1) // C
Ddiv = B // D - (A - 1) // D
gcd_CD = int(C * D / fractions.gcd(C, D))
CDdiv = B // gcd_CD - (A - 1) // gcd_CD
result = int(B - (A - 1) - Cdiv - Ddiv + CDdiv)
print(result)