ININT - Incrementing The Integer

题面翻译

从起点 $1$ 开始，每次选择当前数的任意一位上加上去,例如，从 $23$ 可以得到 $25$ 或 $26$ ,若要用这种方法得到 $100$ ,AB两种方案都可以做到，A方案需要 $21$ 次操作，B方案则只需要 $17$ 次（这也是最少的操作次数）

$A. 1-2-4-8-16-17-18-19-20-22-24-28-36-39-48-56-62-68-76-83-91-100$

$B. 1-2-4-8-16-17-24-28-36-39-48-56-62-68-76-83-91-100$

C方案是另一种只需要 $17$ 次操作的方法：

$C. 1-2-4-8-16-22-24-28-36-39-48-56-62-68-76-83-91-100$

现在，输入几个数，对于每个数，输出最小步骤 $S$ 和解决方案数 $T$。因为 $T$ 可能相当大，所以应该输出 $T$ 对 $1000000007$ 取模的值。

题目描述

Starting from the number '1', every time you can choose a digit from the current number and add it to the number itself. 23, for example, could be changed into 25 or 26. To get 100, using the above scheme, paths A and B are both possible. A requires 21 steps, but B needs only 17 (which is also the minimum)

A. 1-2-4-8-16-17-18-19-20-22-24-28-36-39-48-56-62-68-76-83-91-100 B. 1-2-4-8-16-17-24-28-36-39-48-56-62-68-76-83-91-100

C is another 17 step solution for 100.

C. 1-2-4-8-16-22-24-28-36-39-48-56-62-68-76-83-91-100

Now, you are given several numbers, for each number, print the minimum steps S and number of solutions T. As T could be quite large, you should print T%1000000007 instead.

输入格式

Each line of input contains a integer K as a test case. Input ends with End Of File.

输出格式

For each test case print the minimum steps and solutions in a single line. If it's impossible to get the number, print "IMPOSSIBLE" instead. ( without the quotes ).

样例 #1

样例输入 #1

16
100
87

样例输出 #1

4 1
17 2
IMPOSSIBLE