#include <bits/stdc++.h>
using namespace std;
const long long MXN = 1e6 + 1;
const long long MNN = 1e3 + 1;
const long long MOD = 1e9 + 7;
const long long INF = 1e18;
const long long MAGIC = 1000;
const long double EPS = 1e-9;
vector<int> v;
int n, m, a, b, ans;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  cin >> n >> m >> a >> b;
  int x = min(min(a * n, (n - n % m) / m * b + n % m * a), (n + m) / m * b);
  cout << x;
  return 0;
}

### Prompt

In CPP, your task is to solve the following problem:

Ann has recently started commuting by subway. We know that a one ride subway ticket costs a rubles. Besides, Ann found out that she can buy a special ticket for m rides (she can buy it several times). It costs b rubles. Ann did the math; she will need to use subway n times. Help Ann, tell her what is the minimum sum of money she will have to spend to make n rides?

Input

The single line contains four space-separated integers n, m, a, b (1 ≤ n, m, a, b ≤ 1000) — the number of rides Ann has planned, the number of rides covered by the m ride ticket, the price of a one ride ticket and the price of an m ride ticket. 

Output

Print a single integer — the minimum sum in rubles that Ann will need to spend.

Examples

Input

6 2 1 2


Output

6


Input

5 2 2 3


Output

8

Note

In the first sample one of the optimal solutions is: each time buy a one ride ticket. There are other optimal solutions. For example, buy three m ride tickets.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const long long MXN = 1e6 + 1;
const long long MNN = 1e3 + 1;
const long long MOD = 1e9 + 7;
const long long INF = 1e18;
const long long MAGIC = 1000;
const long double EPS = 1e-9;
vector<int> v;
int n, m, a, b, ans;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  cin >> n >> m >> a >> b;
  int x = min(min(a * n, (n - n % m) / m * b + n % m * a), (n + m) / m * b);
  cout << x;
  return 0;
}

```