Lexicography

An anagram of a string is any string that can be formed using the same letters as the original. (We consider the original string an anagram of itself as well.) For example, the string ACM has the following 6 anagrams, as given in alphabetical order:

ACM AMC CAM CMA MAC MCA

As another example, the string `ICPC` has the following 12 anagrams (in
alphabetical order):

CCIP CCPI CICP CIPC CPCI CPIC ICCP ICPC IPCC PCCI PCIC PICC

Given a string and a rank $K$, you are to determine the $K^{\text {th}}$ such anagram according to alphabetical order.

The input is composed of $T$ test cases ($1 \leqslant T \leqslant 50$).

Each test case will be designated on a single line
containing the original word followed by the desired rank
$K$. Words will use
uppercase letters (i.e., `A` through
`Z`) and will have length at most 16.
The value of $K$ will be
in the range from 1 to the number of distinct anagrams of the
given word.

A line of the form `# 0` designates the end of the
input.

**Warning:** The value of $K$ could be almost $2^{45}$ in the largest tests, so you
should use type `long` in Java, or type
`long long` in C++ to store
$K$.

For each test, display the $K^{\text {th}}$ anagram of the original string.

Sample Input 1 | Sample Output 1 |
---|---|

ACM 5 ICPC 12 REGION 274 # 0 |
MAC PICC IGNORE |