CF1816A.Ian Visits Mary

Ian and Mary are frogs living on lattice points of the Cartesian coordinate plane, with Ian living on $(0,0)$ and Mary living on $(a,b)$ .

Ian would like to visit Mary by jumping around the Cartesian coordinate plane. Every second, he jumps from his current position $(x_p, y_p)$ to another lattice point $(x_q, y_q)$ , such that no lattice point other than $(x_p, y_p)$ and $(x_q, y_q)$ lies on the segment between point $(x_p, y_p)$ and point $(x_q, y_q)$ .

As Ian wants to meet Mary as soon as possible, he wants to jump towards point $(a,b)$ using at most $2$ jumps. Unfortunately, Ian is not good at maths. Can you help him?

A lattice point is defined as a point with both the $x$ -coordinate and $y$ -coordinate being integers.

The first line contains a single integer $t$ ( $1 \le t \le 500$ ) — the number of test cases. The description of test cases follows.

The first and only line of each test case contains two integers $a$ and $b$ ( $1\le a,b\le 10^9$ ) — the coordinates of the lattice point where Mary lives.

For each test case, print an integer $n$ ( $1 \le n \le 2$ ) on the first line, denoting the number of jumps Ian uses in order to meet Mary. Note that you do not need to minimize the number of jumps.

On the $i$ -th line of the next $n$ lines, print two integers $0 \le x_i,y_i \le 10^9$ separated by a space, denoting Ian's location $(x_i,y_i)$ after the $i$ -th jump. $x_n = a$ , $y_n = b$ must hold.

Ian's initial location and his locations after each of the $n$ jumps need not be distinct.

If there are multiple solutions, output any.

In the first test case:

$(0,0) \to (3,4)$

In the second test case:

$(0,0) \to (3,2) \to (4,4)$

In the third test case:

$(0,0) \to (5,3) \to (3,6)$