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())
AdivC = (a-1)//c
BdivC = b//c
AdivD = (a-1)//d
BdivD = b//d
gc = fractions.gcd(c,d)
div = (c*d)//gc
AdivCandD = (a-1)//div
BdivCandD = b//div

divC = BdivC - AdivC
divD = BdivD - AdivD
divCandD = BdivCandD - AdivCandD
ans = b-a+1
ans = ans -(divC+divD-divCandD)
print(ans)