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)

from fractions import gcd


def lcm_base(a, b):
    return (a * b) // gcd(a, b)


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

count_C = B//C - (A+C-1)//C + 1
count_D = B//D - (A+D-1)//D + 1

CD = lcm_base(C, D)
countCD = B//CD - (A+CD-1)//CD + 1

ans = (B-A+1) - count_C - count_D + countCD
print(ans)