Background

Instead of writing a weak background, it is better to create a higher-quality problem.

Problem Description

For integers $n, k$, if there exist a non-negative integer $x$ and a positive integer $y$ such that:

then we call the ordered pair $(x, y)$ an excellent split of $n$ (where $\land$ means and).

Now given non-negative integers $n, k$, please construct any excellent split of $n$, and output the $x$ and $y$ in your construction. In particular, if no such split exists, output -1.

Input Format

This problem has multiple test cases.

The first line contains a positive integer $T$, representing the number of test cases.

The next $T$ lines each contain two non-negative integers, $n, k$.

Output Format

Output a total of $T$ lines. The $i$-th line gives the answer for the $i$-th test case.

3
1 0
13 3
198818800000 122122200000

0 1
8 5
-1

Hint

Sample Explanation

For the first test case, there is only one possible construction.

For the second test case, $(3,10)$ is also a valid construction.

For the third test case, it can be proved that no valid construction exists.

Constraints

"This problem uses bundled tests."

• $\operatorname{Subtask} 1(20\%)$: $n \leq 10^6$.

• $\operatorname{Subtask} 2(40\%)$: $n \leq 10^{12}$.

• $\operatorname{Subtask} 3(40\%)$: no special restrictions.

For $100\%$ of the testdata: $T \leq 5$, $0 \leq n, k \leq 10^{18}$.

Translated by ChatGPT 5