Cipher

A spy exchanges messages with a very efficient cipher. However long a message is, three numbers carry it.

The Department of National Security worked out the rules.

1. A message uses only lowercase English letters and the space character. Every character has an integer called its character volume. A space has volume $1$, a has volume $2$, b has volume $3$, and so on up to z, which has volume $27$. The volume $V$ of a message is the sum of the volumes of the characters in it.
2. A message consists of $W$ words. A word is a consecutive run of lowercase letters, a message has no leading or trailing space, and neighbouring words are separated by exactly one space.
3. For a given $V$ and $W$, let $S$ be the lexicographically sorted list of every message whose volume is $V$ and which consists of exactly $W$ words. A one-based index $I$ can point at one message in $S$.

So when the spy wants to send a message $M$, he computes the volume $V$ and the word count $W$ of $M$, finds the index $I$ of $M$ in the matching list $S$, and sends only the three numbers $V$, $W$, and $I$.

You are given $V$, $W$, and $I$. Decrypt the spy's message, or report that no such message exists.

In the lexicographic comparison the space character comes before every lowercase letter.

The first line contains the number of test cases $T$. ($1 \le T \le 200$)

Each of the next $T$ lines contains three integers separated by spaces: the volume of the message $V$, the number of words $W$, and the index of the message $I$. ($1 \le V \le 75$, $1 \le W \le 20$, $1 \le I \le 10^{18}$)

For each test case, print one line that starts with Case #x: and then the decrypted message. Here $x$ is the test case number starting from $1$. If no message matches the given $V$, $W$, and $I$, print Corrupted! in place of the message.

Sorting every message of volume $7$ that has $2$ words gives five of them: a aa, a c, aa a, b b, c a. Index $3$ therefore points at aa a.

Volume $2$ with $1$ word allows only a. The list holds a single message, so a request for index $2$ means something went wrong.