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
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 9)
MOD = 10 ** 9 + 7

from fractions import gcd

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

A -= 1

lcm = C * D // gcd(C, D)

def calc(x):
    count = 0
    count += x // C
    count += x // D
    count -= x // lcm
    return x - count

ans = calc(B) - calc(A)
print (ans)