Migrated from Lutece 819 Minimum palindrome

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Description

Setting password is very important, especially when you have so many "interesting'' things in F:\TDDOWNLOAD.

We define the safety of a password by a value. First, we find all the substrings of the password. Then we calculate the maximum length of those substrings which, at the meantime, is a palindrome.

A palindrome is a string that will be the same when writing backwards. For example, aba, abba, abcba are all palindromes, but abcab, abab are not.

A substring of $S$ is a continous string cut from $S$. bcd, cd are the substrings of abcde, but acd, ce are not. Note that abcde is also the substring of abcde.

The smaller the value is, the safer the password will be.

You want to set your password using the first $M$ letters from the alphabet, and its length should be $N$. Output a password with the smallest value. If there are multiple solutions, output the lexicographically smallest one.

All the letters are lowercase.

Input

The first line has a number $T$ ($T\leq 15$) , indicating the number of test cases.

For each test case, there is a single line with two integers $M$ and $N$, as described above. ($1 \leq M \leq 26$, $1 \leq N \leq 10^5$)

Output

For test case $X$, output Case #X: first, then output the best password.

Samples

2
2 2
2 3

Case #1: ab
Case #2: aab

Resources

2013 ACM/ICPC Asia Regional Chengdu Online