2024: CF710 - E. Generate a String
[Creator : ]
Description
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 himxseconds to insert or delete a letter 'a' from the text file andyseconds 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.
Initially, the text editor is empty. It takes himxseconds to insert or delete a letter 'a' from the text file andyseconds 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 $n,x,y\ (1≤n≤10^7,\ 1≤x,y≤10^9)$ − the number of letters 'a' in the input file and the parameters from the problem statement.
Output
Print the only integert − the minimum amount of time needed to generate the input file.
Sample 1 Input
8 1 1
Sample 1 Output
4
Sample 2 Input
8 1 10
Sample 2 Output
8