Background

Translated from POI2021-2022R2 Day0 Warm-up Problem.

Problem Description

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 Format

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

Output Format

Output the minimum number of operations.

8 2 1

8

Hint

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 $0$ is the sample.

Translated by ChatGPT 5