A. The Third Three Number Problemtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputEach 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). OutputFor 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.ExampleInput
541122046194723326Output
3 3 1
-1
2 4 6
69 420 666
12345678 87654321 100000000
NoteIn 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.
541122046194723326
3 3 1 -1 2 4 6 69 420 666 12345678 87654321 100000000 
['constructive algorithms', 'math', '*800']