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)

#define _CRT_SECURE_NO_WARNINGS
#include"bits/stdc++.h"
#define INF          1e9
#define INFLL        1e18
#define EPS          1e-9
#define MOD          1000000007
#define REP(i,n)     for(ll i=0,i##_len=(n);i<i##_len;++i)
#define REP1(i,n)    for(ll i=1,i##_len=(n);i<=i##_len;++i)
#define REPR(i,n)    for(ll i=(n)-1;i>=0;--i)
#define REPR1(i,n)   for(ll i=(n);i>0;--i)
#define REPC(i,obj)  for(auto i:obj)
#define ALL(obj)     (obj).begin(),(obj).end()
#define SETP(n)      cout<<fixed<<setprecision(n)
#define VV(T,h,w)    vector<vector<T>>(h,vector<T>(w))
#define VVI(T,h,w,i) vector<vector<T>>(h,vector<T>(w,i))
using namespace std;
using ll = long long;
template<typename T = ll>inline T in() { T ret; cin >> ret; return ret; }

ll howManyDivisers(ll a, ll b, ll m)
{
    ll foo = a + (m - a % m) % m;
    ll bar = b - (b % m);
    if (foo > bar)return 0;
    else return (bar - foo) / m + 1;
}
ll gcd(ll x, ll y)
{
    return y == 0 ? x : gcd(y, x % y);
}
int main()
{
    ll a = in(), b = in(), c = in(), d = in();
    cout <<
        b - a + 1
        - howManyDivisers(a, b, c)
        - howManyDivisers(a, b, d)
        + howManyDivisers(a, b, c / gcd(c, d) * d)
        << endl;
}