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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <algorithm>
#include <numeric>

#define rep(i, n) for(int i = 0; i < (int)(n); i++)
typedef long long ll;
using namespace std;

#ifdef DEBUG
    #define IFD if(true)
#else
    #define IFD if(false)
#endif

ll gcd(ll a, ll b)
{
    if(b == 0) return a;
    return gcd(b, a % b);
}

ll lcm(ll a, ll b)
{
    return a / gcd(a, b) * b;
}

ll f(ll A, ll C, ll D)
{
    return A - (A / C) - (A / D) + A / lcm(C, D);
}

int main()
{
    ll A, B, C, D, ans;
    cin >> A >> B >> C >> D;

    cout << f(B, C, D) - f(A - 1, C, D) << endl;

    return 0;
}