Turning Trominos

$L$-trominos,
replicated.

The $L$-tromino is
composed of three unit squares arranged as shown in part A of
the illustration to the right. The $L$-tromino is also an example of a
*rep-tile* because four $L$-trominos can be arranged to make a
replica of itself that is twice as tall and twice as wide, as
shown in B. Rep-tiles are interesting because, once they can
tile themselves, they can recursively tile as much of the plane
as we want, as suggested in C and D. Part C is made from four
copies of B, and D is made from four copies of C. Figure 1
shows the first quadrant of the plane completely tiled by
$L$-trominos by repeating
the same procedure.

For this problem, you will be given a square in the first quadrant, and your task is to find the orientation of the $L$-tromino covering that square. The unit squares of the first quadrant are numbered $0, 1, 2, \ldots $ in the $x$- and $y$-directions, as shown. The dots, in order from left to right, correspond to the first four sample inputs.

The first line contains an integer $n$ $(1 \leq n \leq 10\, 000)$, indicating the number of cases that follow. Each case consists of a single line. Each of the next $n$ lines contains two integers $x$ and $y$, separated by a space, with $0\leq x,y\leq 2^{60}$, indicating a particular square in the first quadrant.

For each case, output the orientation of the $L$-tromino that covers the given square, one line per case, where the orientations are shown in Figure 2.

Sample Input 1 | Sample Output 1 |
---|---|

5 0 0 1 3 2 7 7 12 100 100 |
0 1 2 3 0 |