Digit Sum Depth

For a positive integer $a$, let $S(a)$ be the sum of the digits of $a$ written in base $l$. Let $L(a)$ be the smallest $k$ with $S^k(a) \leq l-1$, where $S^0(a) = a$ and $S^k(a) = S(S^{k-1}(a))$ for $k \geq 1$.

Given $N$, find the smallest positive integer $a$ with $L(a) = N$ and print that value modulo $m$.

The input has several test cases. Each test case is one line with three integers $N$, $m$, $l$ ($0 \leq N \leq 10^5$, $1 \leq m \leq 10^9$, $2 \leq l \leq 10^9$).

The last line contains 0 0 0. That line is not a test case.

For each test case, print one line of the form Case x: y. Here $x$ is the test case number starting at 1, and $y$ is the smallest such $a$ modulo $m$.