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 math
def gcd(a, b):
    while b > 0:
        a, b = b, a%b
    return a

def lcm(a, b):
    return a*b // gcd(a, b)

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

lcm = lcm(C, D)

# minc = C*math.ceil(A/C)
# maxc = C*math.floor(B/C)
# mind = D*math.ceil(A/D)
# maxd = D*math.floor(B/D)
# minlcm = lcm*math.ceil(A/lcm)
# maxlcm = lcm*math.floor(B/lcm)

 # 1~B
nc1 = math.floor(B/C)
nd1 = math.floor(B/D)
nlcm1 = math.floor(B/lcm)

 # 1~A-1
nc2 = math.floor( (A-1)/C )
nd2 = math.floor( (A-1)/D )
nlcm2 = math.floor( (A-1)/lcm )

#if C > B:
#    nc = 0
#if D > B:
#    nd = 0
#if lcm > B:
#    nlcm = 0

nc = nc1 - nc2
nd = nd1 - nd2
nlcm = nlcm1 - nlcm2

n = B - A + 1 - nc - nd + nlcm

print(n)

 # 何故か不正解、納得いかん