P12336 Third Heart

[Third Heart](https://music.163.com/#/song?id=1849700898).

mikage likes construction problems. One day, she came up with a simple construction problem: Given $a$, try to construct a **quadruple** of positive integers $(a,b,c,d)$ such that: 1. $\sqrt{a^2+b^2+c^2+d^2}=a\oplus b\oplus c\oplus d$. 2. $a

One line containing one integer $a$.

If there is a solution, output three integers $b,c,d$ in one line separated by spaces. If there is no solution, output $-1$.

### Sample Explanation As stated in the problem. ### Constraints This problem uses bundled subtasks. You can get the score of a subtask only if you pass all testdata points in that subtask. |Subtask|Range of $a$|Special Property|Score| | :----------: | :----------: | :----------: |:--:| |0|$a\le 10$|None|5| |1|$a\le 300$|None|5| |2|$a\le 4\times 10^3$|A|10| |3|$a\le 10^7$|B|10| |4|$a\le 2\times 10^8$|C|20| |5|$a\le 10^9$|D|10| |6|$a\le 10^9$|None|40| For all data, $1\le a \le 10^9$. Special Property A: There exists an integer $k\ge 2$ such that $a = 2^k$. Special Property B: $a \equiv 0 \pmod{4}$. Special Property C: $a \equiv 1 \pmod{4}$. Special Property D: There exists an integer $k\ge 2$ such that $a = 2^k-1$. Translated by ChatGPT 5