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
import fractions

A,B,C,D=map(int,input().split())
lcm=int(C*D/(fractions.gcd(C,D)))

if B//lcm==0:
    num_CD=0
else:
    num_CD=B//lcm-math.ceil(A/lcm)+1


if B//C==0:
    num_C=0
else:
    num_C=B//C-math.ceil(A/C)+1



if B//D==0:
    num_D=0
else:
    num_D=B//D-math.ceil(A/D)+1


ans=B-A+1-num_C-num_D+num_CD


print(int(ans))