CF940B.Our Tanya is Crying Out Loud

普及/提高-

通过率：0%

AC君温馨提醒

该题目为【codeforces】题库的题目，您提交的代码将被提交至codeforces进行远程评测，并由ACGO抓取测评结果后进行展示。由于远程测评的测评机由其他平台提供，我们无法保证该服务的稳定性，若提交后无反应，请等待一段时间后再进行重试。

题目描述

Right now she actually isn't. But she will be, if you don't solve this problem.

You are given integers $n$ , $k$ , $A$ and $B$ . There is a number $x$ , which is initially equal to $n$ . You are allowed to perform two types of operations:

Subtract 1 from $x$ . This operation costs you $A$ coins.
Divide $x$ by $k$ . Can be performed only if $x$ is divisible by $k$ . This operation costs you $B$ coins.

What is the minimum amount of coins you have to pay to make $x$ equal to $1$ ?

输入格式

The first line contains a single integer $n$ ( $1<=n<=2·10^{9}$ ).

The second line contains a single integer $k$ ( $1<=k<=2·10^{9}$ ).

The third line contains a single integer $A$ ( $1<=A<=2·10^{9}$ ).

The fourth line contains a single integer $B$ ( $1<=B<=2·10^{9}$ ).

输出格式

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

输入输出样例

输入#1
```
9
2
3
1
```
输出#1
```
6
```
输入#2
```
5
5
2
20
```
输出#2
```
8
```
输入#3
```
19
3
4
2
```
输出#3
```
12
```

说明/提示

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.

首页