A rhyme scheme is the pattern of rhymes at the end of each line of a poem or song. It is usually referred to by using letters to indicate which lines rhyme; lines designated with the same letter all rhyme with each other.
e.g., the following "poem'' of 44 lines has an associated rhyme scheme "ABBA''
1 —— 9999 bugs in the code A
2 —— Fix one line B
3 —— Should be fine B
4 —— 100100 bugs in the code A
This essentially means that line 11 and 44 rhyme together and line 22 and 33 rhyme together.
The number of different possible rhyme schemes for an nn-line poem is given by the Bell numbers. For example, B_3 = 5B3=5, it means there are five rhyme schemes for a three-line poem: AAA, AAB, ABA, ABB, and ABC.
The question is to output the kk-th rhyme scheme in alphabetical order for a poem of nn lines.For example: the first rhyme scheme of a three-line poem is "AAA'', the fourth rhyme scheme of a three-line poem is ABB''.
InputFile
The first line of the input gives the number of test cases, TT (1 \leq T \leq 100001≤T≤10000). TT test cases follow.
Each test case contains a line with two integers nn and kk.
1 \leq n \leq 26, 1 \leq k \leq B_n1≤n≤26,1≤k≤Bn (B_nBn is the nn-th of Bell numbers)
OutputFile
For each test case, output one line containing Case #x: y, where xx is the test case number (starting from 11) and yy is the rhyme scheme contains uppercase letters.
样例输入
7 1 1 2 1 3 1 3 2 3 3 3 4 3 5
样例输出
Case #1: A Case #2: AA Case #3: AAA Case #4: AAB Case #5: ABA Case #6: ABB Case #7: ABC