Problem Statement

There is a grid of $\ N \times M\ $ cells.
Let $\ (i,j)\ $ denote the cell in the $\ i\ $-th row from the top and the $\ j\ $-th column from the left.

You currently have $\ 1\ $ stone, and you place it on any cell you like.
After that, you repeat the following operations $\ 1,2\ $ in the order of operations $\ 1,2,1,2,\cdots\ $, starting from operation $\ 1\ $, and end the process at any time you like.
However, if an operation cannot be performed, the process ends at that point. Note also that it is fine not to perform even $1$ operation.

Operation $\ 1 : $ Move the stone to a cell that shares $\ 1\ $ vertex with the cell where the stone is currently placed, and place the stone on that cell.
(Strictly speaking, move the stone from $\ (i,j)\ $ to one of $\ (i-1,j-1),(i-1,j+1),(i+1,j-1),(i+1,j+1)\ $; however, the stone must not leave the grid.)
Operation $\ 2 : $ Move the stone to a cell that shares $\ 1\ $ edge with the cell where the stone is currently placed, and place the stone on that cell.
(Strictly speaking, move the stone from $\ (i,j)\ $ to one of $\ (i-1,j),(i,j-1),(i,j+1),(i+1,j)\ $; however, the stone must not leave the grid.)

If, at the time you end the process, a stone has been placed on every cell exactly $\ 1\ $ time each, Mitsubachi-kun will be pleased.
Note that when you first place the stone on a cell, that cell is also considered to have had a stone placed on it.

Is there a way to choose the initial position of the stone and perform the operations so that Mitsubachi-kun will be pleased?
If one exists, report how to choose the position of the stone and how to perform the operations; if none exists, report that fact.
If there are multiple ways to choose the initial position of the stone and perform the operations so that Mitsubachi-kun will be pleased, any of them will be accepted.

You are given $\ T\ $ test cases; find the answer for each of them.

Input

$T$

$N\ \ M$

• $1 \leq T \leq 100$
• $1 \leq N,M \leq 1000$
• For each input file, the sum of the maximum of $\ N\ $ and $\ M\ $ over the given test cases does not exceed $\ 1200\ $.
• All inputs are integers.

Output

If there is no way to choose the position of the stone and perform the operations so that Mitsubachi-kun will be pleased, print -1 followed by a newline.

Otherwise, output as follows.

$Q$
$s\ \ t$
$i_1\ \ j_1$
$i_2\ \ j_2$
$\vdots$
$i_Q\ \ j_Q$

Here, $\ Q\ $ represents the total number of operations $\ 1,2\ $.
Also, $\ s,t\ $ indicate that the cell where the stone is first placed is $\ (s,t)\ $, and $i_k,j_k(1 \leq k \leq Q)\ $ indicate that the stone is placed on $\ (i_k,j_k)\ $ after repeating operations $\ 1,2\ $ a total of $\ k\ $ times.
Therefore, your output must satisfy the following constraints.

• $0 \leq Q$
• $1 \leq s,i_k \leq N(1 \leq k \leq Q)$
• $1 \leq t,j_k \leq M(1 \leq k \leq Q)$
• All outputs are integers.

In this case, the output consists of $\ Q+2\ $ lines in total. Also, print a newline at the end.

Do this for all $\ T\ $ test cases.

Sample

2
2 2
1 3

3
1 2
2 1
2 2
1 1
-1

3
1 1
2 2
2 1
1 2

3
1 1
1 2
2 1
2 2

4
1 2
2 1
2 2
1 1
1 2