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)

import sys,heapq,fractions
from collections import deque,defaultdict
printn = lambda x: sys.stdout.write(x)
inn = lambda : int(input())
inl   = lambda: list(map(int, input().split()))
inm   = lambda:      map(int, input().split())
DBG = True  and False
def ddprint(x):
  if DBG:
    print(x)

def foo(x,c,d):
    xc = (x)//c + 1
    xd = (x)//d + 1
    g = c * d // fractions.gcd(c,d)
    xg = (x)//g + 1
    z = x+1-(xc+xd-xg)
    ddprint("x {} c {} d {} xc {} xd {} g {} xg {} z {}".format(x,c,d,xc,xd,g,xg,z))
    return z

a,b,c,d = inm()
print(foo(b,c,d)-foo(a-1,c,d))