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>
using namespace std;
using ll = long long;
const ll MOD = 1000000007;

ll gcd(ll a, ll b) {
  if(a < b) return gcd(b, a);
  ll r;
  while ((r=a%b)) {
    a = b;
    b = r;
  }
  return b;
}

int main(){
    ll A,B,C,D;
    cin >> A >> B >> C >> D;
    ll LCM = (C*D)/gcd(C, D);
    ll toA, toB;
    
    A--;
    toA = A/C + A/D - A/LCM;
    toA = A - toA;
    toB = B/C + B/D - B/LCM;
    toB = B - toB;
    
    cout << toB - toA << "\n";
    return 0;
}