You are in front of a hard grid challenge.
There are a grid, a clock, and of course a coin on the grid. The clock starts counting from the moment number 1, then number 2, and so on. At Each moment you can move the coin according to the following rule:
At each moment $$$i$$$ you can choose an integer number $$$x_i$$$. Let's assume that the coin is at the coordinate $$$(a,b)$$$ at the $$$ith$$$ moment. Now if $$$i$$$ is odd, the coin will jump to the coordinate $$$(a+x_i,b+x_i)$$$. But if $$$i$$$ is even, the coin will jump to the coordinate $$$(a+x_i,b-x_i)$$$.
The challenge is to find the minimum number of moments needed to move the coin from the coordinate $$$(0,0)$$$ to the coordinate $$$(n,m)$$$ and what is the sequence $$$x_i$$$ you have chosen to solve the challenge.
The challenge may be Impossible, so in this case print -1.
The first line contains a single integer $$$t$$$ $$$(1 \le t \le 10^5)$$$, the number of test cases.
At each test case thare are two integers $$$n$$$,$$$m$$$ $$$(-10^9 \le n,m \le 10^9)$$$, the target coordinate $$$(n,m)$$$.
For each test case, Print -1 if it's impossible to reach $$$(n,m)$$$ starting from $$$(0,0)$$$. Otherwise, print the minimum number of moments needed to complete the challenge followed by the chosen numbers during the porocess.
33 32 7-10 8
1 3 -1 2 -1 -9
in the third test case we can reach the position (-10,8) in 2 moves. in the first move we choose $$$x_1=-1$$$ so the new coordinate will be (0-1,0-1) = (-1,-1). in the second move we choose $$$x_1=-9$$$ so the new coordinate will be ((-1)+(-9) , (-1)-(-9)) = (-10,8).
