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)

a,b,c,d =(int(i) for i in input().split())  

import fractions

a1 = a//c
b1 = b//c

r1 = abs(a1-b1)

a2 = a//d
b2 = b//d
r2 = abs(a2-b2)

if a % c == 0:
	r1 += 1

#print(r1)
if a % d == 0:
	r2 += 1
#print(r2)

x = int(c*d/fractions.gcd(c, d))
p = b//x
q = a//x


r = abs(p - q)

if a % x == 0:
	r += 1

#print(r)
print(int((b-a)+1 -(r1 + r2 - r)))