Harmonic Value Description

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 65536/65536 K (Java/Others)

Description

The harmonic value of the permutation $p_1,p_2,\cdots p_n$ is
$$\sum_{i=1}^{n-1} gcd(p_i.p_{i+1})$$
Mr. Frog is wondering about the permutation whose harmonic value is the strictly k-th smallest among all the permutations of [n].

Input

The first line contains only one integer T ($1\leq T\leq 100$), which indicates the number of test cases.

For each test case, there is only one line describing the given integers n and k ($1\leq 2k \leq n \leq10000$).

Output

For each test case, output one line “Case #x: $p_1\ p_2\ \cdots \ p_n$”, where x is the case number (starting from 1) and $p_1\ p_2\ \cdots \ p_n$ is the answer.

Sample Input

2 4 1 4 2

Sample Output

Case #1: 4 1 3 2 Case #2: 2 4 1 3

Hint

wange2014

Source

2016中国大学生程序设计竞赛(长春)-重现赛

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