P14027 【MX-X20-T1】「FAOI-R7」Train Harder

Little C is a hard worker who trains every day. Little C starts with an initial ability value $a$ and aims to reach a target ability value $b$. Both $a$ and $b$ are non-negative integers, and it is guaranteed that $a < b$. There is a positive integer $k$. Each day, Little C can choose one of the following two training methods: - Normal training: After training, Little C's ability value becomes $a + k$. - Train harder: After training, Little C's ability value becomes $a \times k$. Little C wants to know: what is the minimum number of days required to make his ability value greater than or equal to $b$?

Only one line containing two non-negative integers $a$, $b$ and one positive integer $k$, representing the initial ability value, the target ability value, and the parameter for ability growth, respectively.

Output one line containing a positive integer, which is the answer.

### Explanation #1 Choose normal training. After training, the ability value becomes $2 + 2 = 4$, achieving the goal in one day. ### Explanation #2 The training plan is as follows: - On the first day, choose normal training. After training, the ability value becomes $1 + 3 = 4$. - On the second day, choose train harder. After training, the ability value becomes $4 \times 3 = 12$. - On the third day, choose train harder. After training, the ability value becomes $12 \times 3 = 36$. - On the fourth day, choose train harder. After training, the ability value becomes $36 \times 3 = 108$. The goal is achieved in four days. ### Explanation #3 The training plan is as follows: - On the first day, choose normal training. After training, the ability value becomes $0 + 2 = 2$. - On the second day, choose normal training. After training, the ability value becomes $2 + 2 = 4$. - On the third day, choose normal training. After training, the ability value becomes $4 + 2 = 6$. The goal is achieved in three days. ### Data Range For $30\%$ of the data, $2 \le a < b \le 10^3$, $k \ge 2$. For another $20\%$ of the data, $k = 1$. For all data, $0 \le a < b \le 10^6$, $1 \le k \le 10^6$. --- *Translated by DeepSeek V3.1*