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 <bits/stdc++.h>
#define rep(i,n) for(int i=0;i<(n);i++)
using namespace std;
typedef long long ll;
typedef pair<int, int> P;
ll gcd(ll a, ll b) {
    if(a%b==0) return b;
    return gcd(b, a%b);
}
int main(void) {
    ll a, b, c, d; cin >> a >> b >> c >> d;
    ll cd = c/gcd(c,d)*d;
    ll x = b/c - a/c;
    if(a%c==0) x+=1;
    ll y = b/d - a/d;
    if(a%d==0) y+=1;
    ll z = b/cd - a/cd;
    if(a%cd==0) z+=1;
    cout << b-a-(x+y-z)+1;
}