Sparse Rankings

In a N-Ball championship, $N$ teams participate.
Each team has its own home field, where it plays exactly one match against each of the other teams during the tournament.
Thus, the total number of matches is $N \times (N - 1)$ .

Every match ends with a win for one team (no draws). The winner receives 1 point.

At the end of the championship, two tables are prepared:

Tournament Table — an $N \times N$ matrix where:
- For $i \neq = j$ , the cell $(i, j)$ contains the result of the match between team $i$ and team $j$ played on team $i$ ’s home field (Win or Lose from team $i$ ’s perspective).
- Diagonal cells $(i, i)$ are not used.
Rankings — a table listing all teams in descending order of their total points.

Consider this Tournament Table:

	1	2	3	4
1	-	Win	Lose	Lose
2	Win	-	Lose	Win
3	Win	Lose	-	Win
4	Lose	Lose	Lose	-

Team 1 at home: beat Team 2, lost to Teams 3 and 4.
Team 2 at home: beat Teams 1 and 4, lost to Team 3.
Team 3 at home: lost to Team 2, beat Teams 1 and 4.
Team 4 at home: lost all matches.

Thus, the Rankings table after adding all results is:

Team	Score
Team3	5
Team2	4
Team1	2
Team4	1

A Rankings table is called sparse if the difference between the leader’s score and the last-place score is greater than $K$ .

Given $N$ and $K$ , count how many distinct Tournament Tables produce a sparse Rankings table.

Constraints

$2 \leq N \leq 6$
$0 \leq K \leq 9$

Input Format

The first line contains an integer $T$ — the number of test cases.
Each of the next $T$ lines contains a pair of integers $N$ and $K$ .

Output Format

Output $T$ lines. On the $i$ -th line, print Case #i: num, where $n u m$ is the number of Tournament Tables whose Rankings table is sparse for test $i$ .

Example

Input

2
2 0
3 2

Output

Case #1: 2
Case #2: 18

Explanation

For $N = 2$ and $K = 0$ , the following two Tournament Tables produce a sparse Ranking table:

	1	2
1	-	Lose
2	Win	-

	1	2
1	-	Win
2	Lose	-

Each of them result in a table where the team in the first place has 2 points, and the team in the second place has 0 points.