CodeForce 710E

Generate a String

 

　　zscoder wants to generate an input file for some programming competition problem.

His input is a string consisting of n letters 'a'. He is too lazy to write a generator so he will manually generate the input in a text editor.

Initially, the text editor is empty. It takes him x seconds to insert or delete a letter 'a' from the text file and y seconds to copy the contents of the entire text file, and duplicate it.

zscoder wants to find the minimum amount of time needed for him to create the input file of exactly n letters 'a'. Help him to determine the amount of time needed to generate the input.

Input

　　The only line contains three integers n, x and y (1 ≤ n ≤ 10⁷, 1 ≤ x, y ≤ 10⁹) — the number of letters 'a' in the input file and the parameters from the problem statement.

Output

　　Print the only integer t — the minimum amount of time needed to generate the input file.

Examples

Input

 

8 1 1

Output

 

4

Input

 

8 1 10

Output

 

8

题意：
　　给出n（目标字符串有n个‘a’），x（增加或删除一个‘a’需要多少秒），y（复制并粘贴当前的字符串需要多少秒）
求用最少的时间，生成n个‘a’；
思路：
　　dp题目，当n == 0， 1 时需要时间为0， x
　　n为奇数时：可以是 n - 1 加上个‘a’ 或者 n + 1 删除一个‘a’
　　n为偶数时：就得看看 复制一半个‘a’需要的时间长，还是一个一个的加的时间长
　　
AC代码：

# include <bits/stdc++.h>
using namespace std;
typedef long long ll;
ll a, b, n;
ll dp(ll i)
{
    if(i == 0) 
        return 0;
    if(i == 1) 
        return a;
    if(i % 2)
    {
        ll i1 = dp(i - 1), i2 = dp(i + 1);
        return a + min(i1, i2);
    }
    else if(i / 2 * a <= b)
        return i * a;
    else 
        return b + dp(i / 2);
}
int main()
{
    while(~scanf("%I64d", &n))
    {
        scanf("%I64d%I64d", &a, &b);
        printf("%I64d
", dp(n));
    }
    return 0;
}