Codeforces Round #466 (Div. 2) B. Our Tanya is Crying Out Loud[将n变为1，有两种方式,求最小花费/贪心]

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.

[题意]:将n变为1，有两种方式① n-1花费a , ② 如果n能够被k整除，n=n/k,花费b.求最小花费.

[分析]:很显然这是道贪心题，
一个很容易错的地方就是想着优先除二，然后在减一，
因为没有考虑两者的花费，如果b很大的话就错了，所以每次都要判断下，然后注意细节就行了

首先如果k==1，那么ans=(n-1)*a;

n%k!=0,只能执行操作1

n<k,只能执行操作1
n%k==0(n>=k) 的情况下比较n到达相同结果时两种操作的花费即可。

[代码]:

/*
题意：将n变为1，有两种方式①n-1花费a,②如果n能够被k整除，n=n/k,花费b,求最小花费
*/
/*
很显然这是道贪心题，
一个很容易错的地方就是想着优先除二，然后在减一，
因为没有考虑两者的花费，如果b很大的话就错了，所以每次都要判断下，然后注意细节就行了
*/
#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define mem(a) memset(a,0,sizeof(a))
typedef long long ll;
typedef pair<int,int> pii;
const int maxn=;
const int inf=0x3f3f3f3f;
int main()
{
    ll x,n,k,a,b,ans;
    while(~scanf("%lld%lld%lld%lld",&n,&k,&a,&b)){
        ans=;
        if(k==) return *printf("%lld\n",a*(n-));  //注意特判k==1的情况，防止死循环
        while(n!=){
            //n无法整除k
            if(n%k!=){    //不能整除只能减法(a)，减到整除为止
                ans+=a*(n%k);
                n-=(n%k);
            }
            if(n<k){       //此时只能减法(a)，除法永远用不到，直接求解答案
                ans+=a*(n-);
                break;
            }
            //n可以整除k
            ans+=min(b,a*(n-n/k)); //减法(a)和除法(b)取最小花费
            n/=k; //n可以整除k
        }
        printf("%lld\n",ans);
    }
}
/*
n-n/k*k = n%k
获取距离n最近的k的倍数的方法是:n/k*k = n-n%k
*/

贪心