The Third Three Number Problem

Description:

Input:

Each test contains multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. The following lines contain the descriptions of the test cases.

The only line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 10^9$$$).

Output:

For each test case, print any three integers $$$a$$$, $$$b$$$ and $$$c$$$ ($$$0 \le a, b, c \le 10^9$$$) for which $$$(a\oplus b)+(b\oplus c)+(a\oplus c)=n$$$. If no such integers exist, print $$$-1$$$.

Sample Input:

5
4
1
12
2046
194723326

Sample Output:

3 3 1
-1
2 4 6
69 420 666
12345678 87654321 100000000

Note:

In the first test case, $$$a=3$$$, $$$b=3$$$, $$$c=1$$$, so $$$(3 \oplus 3)+(3 \oplus 1) + (3 \oplus 1)=0+2+2=4$$$.

In the second test case, there are no solutions.

In the third test case, $$$(2 \oplus 4)+(4 \oplus 6) + (2 \oplus 6)=6+2+4=12$$$.