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

def lcm(C, D):
    return (C * D) // math.gcd(C, D)

lcm_C_D = lcm(C,D)
rem_C = lcm_C_D // C
rem_D = lcm_C_D // D

lcm_count = rem_C + rem_D - 1


rem_A = A % lcm_C_D
dif_A = lcm_C_D - rem_A
count_A_C = dif_A // C
count_A_D = dif_A // D
before_count = count_A_C + count_A_D + 1



dif_B = B % lcm_C_D
count_B_C = dif_B // C
count_B_D = dif_B // D
after_count = count_B_C + count_B_D 


syou_A = (A + dif_A) // lcm_C_D
syou_B = (B - dif_B) // lcm_C_D
between_count = (syou_B - syou_A) * lcm_count


print(B - A + 1 - (after_count + between_count + before_count))