Our Tanya is Crying Out Loud

Description:

Input:

The first line contains a single integer n (1 ≤ n ≤ 2·10⁹).

The second line contains a single integer k (1 ≤ k ≤ 2·10⁹).

The third line contains a single integer A (1 ≤ A ≤ 2·10⁹).

The fourth line contains a single integer B (1 ≤ B ≤ 2·10⁹).

Output:

Output a single integer — the minimum amount of coins you have to pay to make x equal to 1.

Sample Input:

9
2
3
1

Sample Output:

6

Sample Input:

5
5
2
20

Sample Output:

8

Sample Input:

19
3
4
2

Sample Output:

12

Note:

In the first testcase, the optimal strategy is as follows:

• Subtract 1 from x (9 → 8) paying 3 coins.
• Divide x by 2 (8 → 4) paying 1 coin.
• Divide x by 2 (4 → 2) paying 1 coin.
• Divide x by 2 (2 → 1) paying 1 coin.

The total cost is 6 coins.

In the second test case the optimal strategy is to subtract 1 from x 4 times paying 8 coins in total.