Harmonic Value Description
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)Total Submission(s): 724 Accepted Submission(s): 380
Special Judge
Problem 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].
$$\sum_{i=1}^{n-1} gcd(p_i.p_{i+1})$$
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 ($1\leq 2k \leq n \leq10000$).
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