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 ALL(a) (a).begin(), (a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define pb push_back
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define rep(i, n) FOR(i, 0, n)
#define ll long long
using namespace std;

const ll P = 1000000007;
ll gcd(ll a, ll b) { return b != 0 ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }

int main()
{
  cout << fixed << setprecision(10);
  ll A,B,C,D;
  cin >> A >> B >> C >> D;
  ll E = (A-1)/C;
  ll F = (A-1)/D;
  ll G = lcm(C,D);
  ll H = (A-1)/G;
  ll I = B/C;
  ll J = B/D;
  ll K = B/G;
  ll L = B - I - J + K;
  ll M = A - E - F + H - 1;
  cout << L - M << endl;
  return 0;
}