Required Length
题意翻译
给定两个正整数n,x,对于每个x,在其中截取一位10进制数字y,与x相乘得到x’, 按上述操作,求出当x的位数与n相等时的最少操作次数
题目描述
You are given two integer numbers, $ n $ and $ x $ . You may perform several operations with the integer $ x $ .
Each operation you perform is the following one: choose any digit $ y $ that occurs in the decimal representation of $ x $ at least once, and replace $ x $ by $ x \cdot y $ .
You want to make the length of decimal representation of $ x $ (without leading zeroes) equal to $ n $ . What is the minimum number of operations required to do that?
输入输出格式
输入格式
The only line of the input contains two integers $ n $ and $ x $ ( $ 2 \le n \le 19 $ ; $ 1 \le x < 10^{n-1} $ ).
输出格式
Print one integer — the minimum number of operations required to make the length of decimal representation of $ x $ (without leading zeroes) equal to $ n $ , or $ -1 $ if it is impossible.
输入输出样例
输入样例 #1
2 1
输出样例 #1
-1
输入样例 #2
3 2
输出样例 #2
4
输入样例 #3
13 42
输出样例 #3
12
说明
In the second example, the following sequence of operations achieves the goal:
1. multiply $ x $ by $ 2 $ , so $ x = 2 \cdot 2 = 4 $ ;
2. multiply $ x $ by $ 4 $ , so $ x = 4 \cdot 4 = 16 $ ;
3. multiply $ x $ by $ 6 $ , so $ x = 16 \cdot 6 = 96 $ ;
4. multiply $ x $ by $ 9 $ , so $ x = 96 \cdot 9 = 864 $ .