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 fractions

numA, numB, numC, numD = map(int, input().split())

AsplitC = int((numA - 1) // numC)
BsplitC = int(numB // numC)
AsplitD = int((numA - 1) // numD)
BsplitD = int(numB // numD)
AsplitCandD = int((numA - 1) // int(numC * numD // fractions.gcd(numC, numD)))
BsplitCandD = int(numB // int(numC * numD // fractions.gcd(numC, numD)))

count = (numB - numA + 1) - ((BsplitC - AsplitC) + (BsplitD - AsplitD) - (BsplitCandD - AsplitCandD))

print(count)