New Self-describing Sequence

Let $a_1, a_2$,... be an integer sequence beginning with $a_1$ = 1. For n ≥ 1, $a_n$+1 is the sum of an and the sum of digits of $a_n$. That’s why we name the sequence a new Self-describing sequence.
The sequence starts with 1, 2, 4, 8, 16, 23, 28, 38, 49, ... and we also define the prefix sum $s_n = a_1 + a_2 + ... + a_n$.
For given positive integer n, find $a_n$ and $s_n$.

The first line of input consists an integer T (T ≤ 32768), indicating the total number of test cases. Each of the following T lines provides an integer n (n ≤ 10^17).

For each test case output its case label first. Then for given n, output $a_n$ and $s_n$. Since the prefix sum is large,you only need to output $s_n$ mod 1000000009. However you should output $a_n$ as its exact value.

7
6
66
666
6666
66666
123456789
31415926535897932

Case #1: 23 54
Case #2: 752 20862
Case #3: 10949 3407733
Case #4: 136193 441127485
Case #5: 1698899 717710112
Case #6: 5061289531 990040993
Case #7: 2508156610654066874 660828136

2017ACM/ICPC亚洲区沈阳站-重现赛（感谢东北大学）