P9863 [POI 2021/2022 R2] arm

Translated from [POI2021-2022R2 Day0 Warm-up Problem](https://szkopul.edu.pl/problemset/problem/gxeCvLD1xW1t-Y33bbC0n3wZ/statement/).

Initially, you have $1$ item. You need to increase the number of items to $> n$ by performing the following step multiple times. - Option $1$: Store the current number of items into the database, costing $a$ time. - Option $2$: Increase the number of items by an amount equal to the number stored in the database, costing $b$ time. Initially, the database is empty. Find the minimum number of operations.

Input one line with three integers $n,a,b\ (1 \leq n \leq 10^{18},1 \leq a,b \leq 10^9)$.

Output the minimum number of operations.

Explanation of the sample: Initially, you have one item. First, perform one scan, costing $2$ time. Then print $2$ times, costing $1 \times 2 = 2$ time, and the number increases to $3$. Continue with another scan, costing $2$ time. Finally, print $2$ more times, costing $1 \times 2 = 2$ time, and the number becomes $9$. Subtask distribution: | Subtask ID | Special Property | Points | | :-----------: | :-----------: | :-----------: | | $1$ | $a = b = 1$ | $10$ | | $2$ | $n \leq 10^3$ | $40$ | | $3$ | $n \leq 10^5$ | $15$ | | $4$ | $n \leq 10^9$ | $15$ | | $5$ | No special constraints | $20$ | Subtask $0$ is the sample. Translated by ChatGPT 5