Problem Statement

Given a binary string of length n, and given that there are k ones in the string, please determine all possible integers that can be represented by the string.

Input Specification

The first line of the input gives the number of test cases, ~T~, and then ~T~ test cases follow.

Each test case consists one line of two integers, ~n~ and ~k~, separated by a space

Output Specification

For each test case, output one line containing Case #x: y, where ~x~ is the case number(starting from 1) and ~y~ is a list consisting of all possible integers in ascending order.

Constraints

~1 \leq T \leq 100~

~1 \leq n \leq 16~

~0 \leq k \leq n~

Sample Input

2
8 1
4 2

Sample Output

Case #1: [1, 2, 4, 8, 16, 32, 64, 128]
Case #2: [3, 5, 6, 9, 10, 12]

Explaination

Case #1:
    0 0 0 0 0 0 0 1 -> 1
    0 0 0 0 0 0 1 0 -> 2
    0 0 0 0 0 1 0 0 -> 4
    0 0 0 0 1 0 0 0 -> 8
    0 0 0 1 0 0 0 0 -> 16
    0 0 1 0 0 0 0 0 -> 32
    0 1 0 0 0 0 0 0 -> 64
    1 0 0 0 0 0 0 0 -> 128
Case #2:
    0 0 1 1 -> 3
    0 1 0 1 -> 5
    1 0 0 1 -> 9
    0 1 1 0 -> 6
    1 0 1 0 -> 10
    1 1 0 0 -> 12

Hint

recursion for-loop combination