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 <vector>
#include <algorithm>
#include <queue>
#include <cstring>
#include <cstdio>
#include <cmath>
#include <set>
#include <map>
#include <bitset>
#include <deque>
#include <numeric>
using namespace std;
using ll = long long;
using itn = int;
const ll MOD = 1000000007;
const ll INF = MOD * MOD;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

ll dp[100010];

ll gcd(ll c, ll d) {
    if (d == 0)
        return c;

    return gcd(d, c % d);
}

ll lcm(ll c, ll d) {
    return c * d / gcd(c, d);
}

int main() {

    ll a, b, c, d;
    cin >> a >> b >> c >> d;

    ll s;

    s = lcm(c, d);

    ll count1;
    ll count2;
    ll ans;

    count1 = b - (b / c + b / d - b / s);
    count2 = a-1 - ((a-1) / c + (a-1) / d - (a-1) / s);
    
    ans = count1 - count2;
    

    cout << ans << endl;

    return 0;

}