You are given two integers $a$ and $b$. You are allowed to perform the following operation any number of times (including zero):

• choose any integer $x$ such that $0 \le x \le a$ (the current value of $a$, not initial),
• set $a := a \oplus x$. Here, $\oplus$ represents the bitwise XOR operator.

After performing a sequence of operations, you want the value of $a$ to become exactly $b$.

Find a sequence of at most $100$ operations (values of $x$ used in each operation) that transforms $a$ into $b$, or report that it is impossible.

Note that you are not required to find the minimum number of operations, but any valid sequence of at most $100$ operations.

Input

The first line of input contains a single integer $t$ ($1 \le t \le 1000$) — the number of test cases.

Each test case contains two integers $a$ and $b$ ($1 \le a, b \le 10^9$).

Output

For each test case, if it is impossible to obtain $b$ from $a$ using the allowed operations, print a single line containing $-1$.

Otherwise, on the first line print a single integer $k$ ($0 \le k \le 100$) — the number of operations. On the second line print $k$ integers ($x_1, x_2, \dots , x_k$) — the chosen values of $x$ in the order you apply them.

If there are multiple valid sequences, you may print any one of them.

Note

For the first test case,

• choose $x = 7$, now $a$ becomes equal to $9 \oplus 7 = 14$.
• choose $x = 8$, now $a$ becomes equal to $14 \oplus 8 = 6$.

Thus, we can make $a = b$.

For the fourth test case, choosing $x = 5$ makes $a = b$.

Samples

6
9 6
13 13
292 929
405 400
998 244
244 353

2
7 8
0
-1
1
5
2
25 779
-1