#P1699A. The Third Three Number Problem
The Third Three Number Problem
Description
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 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 $-1$.
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 $-1$.
Samples
5
4
1
12
2046
194723326
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, $(2 \oplus 4)+(4 \oplus 6) + (2 \oplus 6)=6+2+4=12$.