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)

# -*- coding utf-8 -*-
import fractions

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

lcm = int(C * D / fractions.gcd(C, D))

a_cd = (A - 1) // (lcm)
b_cd = B // (lcm)

a_c = (A - 1) // C
a_d = (A - 1) // D
b_c = B // C
b_d = B // D

a = a_c + a_d - a_cd
b = b_c + b_d - b_cd

print(B - A + 1 - (b - a))