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

maxC = B // C
maxD = B // D
maxlcm = B // lcm

minC = (A-1) // C
minD = (A-1) // D
minlcm = (A-1) // lcm

lcmB = (maxC + maxD - maxlcm)
lcmA = (minC + minD - minlcm)

print((B-A+1)-(lcmB-lcmA))