[Solution] The Third Three Number Problem Codeforces Solution

A. The Third Three Number Problem

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given a positive integer n$n$. Your task is to find any three integers a$a$, b$b$ and c$c$ (0≤a,b,c≤109$0\le a,b,c\le {10}^9$) for which (a⊕b)+(b⊕c)+(a⊕c)=n$(a\oplus b)+(b\oplus c)+(a\oplus c)=n$, or determine that there are no such integers.

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Here a⊕b$a\oplus b$ denotes the bitwise XOR of a$a$ and b$b$. For example, 2⊕4=6$2\oplus 4=6$ and 3⊕1=2$3\oplus 1=2$.

Input

Each test contains multiple test cases. The first line contains a single integer t$t$ (1≤t≤104$1\le t\le {10}^4$) — the number of test cases. The following lines contain the descriptions of the test cases.

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The only line of each test case contains a single integer n$n$ (1≤n≤109$1\le n\le {10}^9$).

Output

For each test case, print any three integers a$a$, b$b$ and c$c$ (0≤a,b,c≤109$0\le a,b,c\le {10}^9$) for which (a⊕b)+(b⊕c)+(a⊕c)=n$(a\oplus b)+(b\oplus c)+(a\oplus c)=n$. If no such integers exist, print −1$-1$.