A certain bathroom has ~N + 2~ stalls in a single row; the stalls on the left and right ends are permanently occupied by the bathroom guards. The other ~N~ stalls are for users.

Whenever someone enters the bathroom, they try to choose a stall that is as far from other people as possible. To avoid confusion, they follow deterministic rules: For each empty stall ~S~, they compute two values ~L_S~ and ~R_S~, each of which is the number of empty stalls between ~S~ and the closest occupied stall to the left or right, respectively. Then they consider the set of stalls with the farthest closest neighbor, that is, those ~S~ for which ~\min(L_S, R_S)~ is maximal. If there is only one such stall, they choose it; otherwise, they choose the one among those where ~\max(L_S, R_S)~ is maximal. If there are still multiple tied stalls, they choose the leftmost stall among those.

~K~ people are about to enter the bathroom; each one will choose their stall before the next arrives. Nobody will ever leave.

When the last person chooses their stall ~S~, what will the values of ~\max(L_S, R_S)~ and ~\min(L_S, R_S)~ be?

Input Specification

The first line of the input gives the number of test cases, ~T~. ~T~ lines follow. Each line describes a test case with two integers ~N~ and ~K~, as described above.

Output Specification

For each test case, output one line containing Case #x: y z, where ~x~ is the test case number (starting from 1), ~y~ is ~\max(L_S, R_S)~, and ~z~ is ~\min(L_S, R_S)~ as calculated by the last person to enter the bathroom for their chosen stall ~S~.

Limits

~1 \le T \le 100~.

~1 \le K \le N~.

Time limit: 60 seconds per test set.

Memory limit: 1GB.

Small Dataset 1

~1 \le N \le 1\,000~.

Small Dataset 2

~1 \le N \le 10^{6}~.

Large Dataset

~1 \le N \le 10^{18}~.

Sample Input

5
4 2
5 2
6 2
1000 1000
1000 1

Sample Output

Case #1: 1 0
Case #2: 1 0
Case #3: 1 1
Case #4: 0 0
Case #5: 500 499

In Sample Case #1, the first person occupies the leftmost of the middle two stalls, leaving the following configuration (O stands for an occupied stall and . for an empty one): O.O..O. Then, the second and last person occupies the stall immediately to the right, leaving 1 empty stall on one side and none on the other.

In Sample Case #2, the first person occupies the middle stall, getting to O..O..O. Then, the second and last person occupies the leftmost stall.

In Sample Case #3, the first person occupies the leftmost of the two middle stalls, leaving O..O...O. The second person then occupies the middle of the three consecutive empty stalls.

In Sample Case #4, every stall is occupied at the end, no matter what the stall choices are.

In Sample Case #5, the first and only person chooses the leftmost middle stall.