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: Wrong Answer)

import fractions

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

s = B - A + 1

if A % C == 0 or A % D == 0:
    A -= 1

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

E = lcm(C, D)

val1 = A // C
val2 = B // C
val3 = A // D
val4 = B // D
val5 = A // E
val6 = B // E

print(s - (val2 - val1 + val4 - val3 - (val6 - val5)))

print("val1 : " + str(val1))
print("val2 : " + str(val2))
print("val3 : " + str(val3))
print("val4 : " + str(val4))
print("val5 : " + str(val5))
print("val6 : " + str(val6))