CF1699A 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 $ .