B. Our Tanya is Crying Out Loud

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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:

1. Subtract 1 from x. This operation costs you A coins.
2. 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?

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.

Examples

Input

Copy

9 2 3 1

Output

6

Input

Copy

5 5 2 20

Output

8

Input

Copy

19 3 4 2

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.

 

分析：贪心。注意判断k==1的情况。

#include
        
         using namespace std;int main(){    long long N,k,A,B;    scanf("%lld%lld%lld%lld",&N,&k,&A,&B);    long long ans=0;    if(k==1)    {        printf("%lld\n",A*(N-1));        return 0;    }    while(N>=k)    {        if(N%k==0)        {            long long next=N/k;            if((N-next)*A>B) ans+=B;            else ans+=(N-next)*A;            N=next;        }        else        {            long long t=N/k;            long long temp=N-t*k;            ans+=A*temp;            N=t*k;        }    }    if(N!=1)//N