Cf:a. the third three number problem

analysis

In the course of the game, I created the XOR distribution law , Directly put yourself speechless
First of all, we should make good use of the nature of XOR
a ^ 0 = a
a ^ a = 0
if a ^ b = c be c ^ b = a
^ There is a law of association, not a law of distribution
therefore , about a Even numbers , obviously a // 2, 0, 0 It's a set of solutions , I'm dizzy

About a It is the proof that odd numbers are not tenable

About a + b and a ^ b Proof of parity

if a + b It's me , explain a and b With the odd and even , The last one is the same , therefore a ^ b And then finally 0, therefore a ^ b Even
if a + b It's strange , explain a and b The last one is different , therefore a ^ b And then finally 1, therefore a ^ b Is odd

With the help of the above lemma , It is known that (a ^ b) + (b ^ c) + (c ^ a) = n
And then there is (a ^ b) ^ (b ^ c) = a ^ c
So the initial formula can be reduced to x + y + (x ^ y) = n
obviously n It's even
speechless

ac code

import sys
input = sys.stdin.readline

for _ in range(int(input())):
    n = int(input())
    if n % 2 == 1:
        print(-1)
    else:
        print(n // 2, 0, 0)

summary

Bit operation fails
Math doesn't work