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: Runtime Error)

import math

def lcm(x, y):
    return (x * y) // math.gcd(x, y)


A,B,C,D = map(int,input().split())
E = lcm(C,D)
c = (A-1)//C + 1 if C!=1 else A
d = (A-1)//D + 1 if D!=1 else A
e = (A-1)//E + 1 if E!=1 else A
cde = [[c,C], [d,D], [e,E]]
cnt_cde = []
for x,y in cde:
    if x*y < B:
        cnt_cde.append((B-x*y)//y+1)
    elif x*y == B:
        cnt_cde.append(1)
    else :
        cnt_cde.append(0)
answer = B-A+1-(cnt_cde[0]+cnt_cde[1]-cnt_cde[2])
print(answer)