#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:167177216")
using namespace std;
const int INF = 1e9;
const long double eps = 1e-9;
const long long MOD = (long long)(INF + 7);
const long long INF64 = (long long)(INF) * (long long)(INF);
const int ddx[] = {-1, 1, 1, -1};
const int ddy[] = {1, 1, -1, -1};
const int dx[] = {-1, -1, 0, 1, 1, 1, 0, -1};
const int dy[] = {0, 1, 1, 1, 0, -1, -1, -1};
const int dx4[] = {-1, 0, 1, 0};
const int dy4[] = {0, 1, 0, -1};
const int dxh[] = {-1, -1, -1, 1, 1, 1, 1, -1};
const int dyh[] = {1, -1, -1, -1, -1, 1, 1, 1};
const string dirs[] = {"RIGHT", "UP", "LEFT", "DOWN"};
bool in(int i, int j, int n, int m) {
  return i >= 1 && i <= n && j >= 1 && j <= m;
}
int main() {
  int n, m, a, b;
  cin >> n >> m >> a >> b;
  int ans = INF;
  for (int i = 0; i <= 1000; i++) {
    for (int j = 0; j <= 1000; j++) {
      int cnt = i * m + j;
      int cur = j * a + i * b;
      if (cnt >= n) ans = min(ans, cur);
    }
  }
  cout << ans << endl;
  return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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>
#pragma comment(linker, "/STACK:167177216")
using namespace std;
const int INF = 1e9;
const long double eps = 1e-9;
const long long MOD = (long long)(INF + 7);
const long long INF64 = (long long)(INF) * (long long)(INF);
const int ddx[] = {-1, 1, 1, -1};
const int ddy[] = {1, 1, -1, -1};
const int dx[] = {-1, -1, 0, 1, 1, 1, 0, -1};
const int dy[] = {0, 1, 1, 1, 0, -1, -1, -1};
const int dx4[] = {-1, 0, 1, 0};
const int dy4[] = {0, 1, 0, -1};
const int dxh[] = {-1, -1, -1, 1, 1, 1, 1, -1};
const int dyh[] = {1, -1, -1, -1, -1, 1, 1, 1};
const string dirs[] = {"RIGHT", "UP", "LEFT", "DOWN"};
bool in(int i, int j, int n, int m) {
  return i >= 1 && i <= n && j >= 1 && j <= m;
}
int main() {
  int n, m, a, b;
  cin >> n >> m >> a >> b;
  int ans = INF;
  for (int i = 0; i <= 1000; i++) {
    for (int j = 0; j <= 1000; j++) {
      int cnt = i * m + j;
      int cur = j * a + i * b;
      if (cnt >= n) ans = min(ans, cur);
    }
  }
  cout << ans << endl;
  return 0;
}

```