As punishment for being naughty, Dante has been trapped in a strange house with many rooms. The house is an $N\times N$ grid of rooms, with $N$ odd and greater than $1$. The upper left room is numbered $1$, and then the other rooms are numbered $2,3,\dots ,N^2$, in a clockwise spiral pattern. That is, the numbering proceeds along the top row of the grid and then makes a 90 degree turn to the right whenever a grid boundary or an already numbered room is encountered, and finishes in the central room of the grid. Because $N$ is odd, there is always a room in the exact center of the house, and it is always numbered $N^2$.

For example, here are the room numberings for houses with $N=3$ and $N=5$:

Dante starts off in room $1$ and is trying to reach the central room (room $N^2$). Throughout his journey, he can only make moves from his current room to higher-numbered, adjacent rooms. (Two rooms must share an edge — not just a corner — to be adjacent.)

Dante knows that he could walk from room to room in consecutive numerical order — i.e., if he is currently in room $x$, he would move to room $x+1$, and so on. This would take him exactly $N^2-1$ moves. But Dante wants to do things his way! Specifically, he wants to reach the central room in exactly $K$ moves, for some $K$ strictly less than $N^2-1$.

Dante can accomplish this by taking one or more shortcuts. A shortcut is a move between rooms that are not consecutively numbered.

For example, in the $5\times 5$ house above,

• If Dante is at $1$, he cannot move to $17$, but he can move to $2$ or to $16$. The move to $2$ is not a shortcut, since $1+1=2$. The move to $16$ is a shortcut, since $1+1\ne 16$.
• From $2$, it is possible to move to $3$ (not a shortcut) or to $17$ (a shortcut), but not to $1$, $16$, or $18$.
• From $24$, Dante can only move to $25$ (not a shortcut).
• It is not possible to move out of room $25$.

As a specific example using the $5\times 5$ house above, suppose that $K=4$. One option is for Dante to move from $1$ to $2$, then move from $2$ to $17$ (which is a shortcut), then move from $17$ to $18$, then move from $18$ to $25$ (which is another shortcut). This is illustrated below (the red arrows represent shortcuts):

Can you help Dante find a sequence of exactly $K$ moves that gets him to the central room, or tell him that it is impossible?

Input Specification

The first line of the input gives the number of test cases, $T$. $T$ test cases follow. Each test case consists of one line with two integers $N$ and $K$, where $N$ is the dimension of the house (i.e. the number of rows of rooms, which is the same as the number of columns of rooms), and $K$ is the exact number of moves that Dante wants to make while traveling from room $1$ to room $N^2$.

Output Specification

For each test case, output one line containing Case #x: y, where $x$ is the test case number (starting from $1$).

If no valid sequence of exactly $K$ moves will get Dante to the central room, $y$ must be IMPOSSIBLE.

Otherwise, $y$ must be an integer: the number of times that Dante takes a shortcut, as described above. (Notice that because Dante wants to finish in strictly less than $N^2-1$ moves, he must always use at least one shortcut.) Then, output $y$ more lines of two integers each. The $i^{\text{th}}$ of these lines represents the $i^{\text{th}}$ time in Dante's journey that he takes a shortcut, i.e., he moves from some room $a_i$ to another room $b_i$ such that $a_i+1<b_i$.

Notice that because these lines follow the order of the journey, $a_i<a_{i+1}$ for all $1\le i<y$.

Limits

$1\le T\le 100$.

$1\le K<N^2-1$.

$Nmod2\equiv 1$. ($N$ is odd.)

Test Set 1

Time limit: 5 seconds.

$3\le N\le 9$.

Test Set 2

Time limit: 20 seconds.

$3\le N\le 39$.

Test Set 3

Time limit: 20 seconds.

$3\le N\le 9999$.

Sample Input

4
5 4
5 3
5 12
3 1

Sample Output

Case #1: 2
2 17
18 25
Case #2: IMPOSSIBLE
Case #3: 2
11 22
22 25
Case #4: IMPOSSIBLE

Sample Case #1 is described in the problem statement. Dante's route is $1\to 2\to 17\to 18\to 25$. Because $1\to 2$ and $17\to 18$ are moves between consecutively numbered rooms, they are not included in the output. Only the shortcuts ($2\to 17$ and $18\to 25$) are included.

In Sample Case #2, there is no solution. (Recall that there is no way for Dante to move diagonally.)

In Sample Case #3, observe that $22$ appears both as the end of one shortcut and the start of the next. It would not be valid to include the line 11 22 25 in the output; each line must represent a single shortcut.

The image shows a $5\times 5$ grid of rooms numbered as described in the statement. A path with arrows is shown as described above. The arrows between $11$ and $22$ as well as $22$ and $25$ are red to show they are shortcuts.

There is another solution that uses only one shortcut: Dante can move from $1\to 2\to 3\to 4\to 5\to 6$, then move from $6\to 19$ (a shortcut), then move from $19\to 20\to 21\to 22\to 23\to 24\to 25$. This is also valid; there is no requirement to minimize (or maximize) the number of shortcuts taken.

In Sample Case #4, Dante cannot get to the central room ($9$, in this case) in just one move.

Note

This problem has different time limits for different batches. If you exceed the Time Limit for any batch, the judge will incorrectly display >20.000s regardless of the actual time taken. Refer to the Limits section for batch-specific time limits.