Problem H
Point Coloring

You are coloring points on an infinite grid. All points are initially colored with color $-1$. You color the point $(0, 0)$ with color $0$, and then, for each $i \geq 0$ in order, do the following:

• Let $S$ be the set of points currently colored with color $i$.

• For each point $(x, y)$ in $S$, color the points $(x + 2^ i, y)$ and $(x, y + 2^ i)$ with color $i+1$

You are given integers $x$ and $y$. At the end of this infinite process, what color will the point $(x, y)$ be?

Input

The first line of the input contains a single integer $t$ ($1 \le t \le 10^5$) —the number of test cases. The description of the test cases follows.

Each test case consists of a single line with two integers $x$ and $y$ ($0 \le x, y \le 10^{18}$) —the coordinates of the point to query.

Output

For each test case, output a single integer —the color of the point $(x, y)$ after this infinite process.

8
0 0
0 1
1 1
3 4
10 8
17 14
0 524287
999926342823684562 152995161783162413

0
1
-1
3
-1
5
19
60