A15244. The Third Three Number Problem

You are given a positive integer $n$ . Your task is to find any three integers $a$ , $b$ and $c$ ( $0 \le a, b, c \le 10^9$ ) for which $(a\oplus b)+(b\oplus c)+(a\oplus c)=n$ , or determine that there are no such integers.

Here $a \oplus b$ denotes the [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of $a$ and $b$ . For example, $2 \oplus 4 = 6$ and $3 \oplus 1=2$ .

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 $n$ ( $1 \le n \le 10^9$ ).

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 $-1$ .

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, $(2 \oplus 4)+(4 \oplus 6) + (2 \oplus 6)=6+2+4=12$ .