Solve the programming task below in a Python markdown code block.
It is the easy version of the problem. The only difference is that in this version $k = 3$.

You are given a positive integer $n$. Find $k$ positive integers $a_1, a_2, \ldots, a_k$, such that:

$a_1 + a_2 + \ldots + a_k = n$

$LCM(a_1, a_2, \ldots, a_k) \le \frac{n}{2}$

Here $LCM$ is the least common multiple of numbers $a_1, a_2, \ldots, a_k$.

We can show that for given constraints the answer always exists.


-----Input-----

The first line contains a single integer $t$ $(1 \le t \le 10^4)$  — the number of test cases.

The only line of each test case contains two integers $n$, $k$ ($3 \le n \le 10^9$, $k = 3$).


-----Output-----

For each test case print $k$ positive integers $a_1, a_2, \ldots, a_k$, for which all conditions are satisfied.


-----Examples-----

Input
3
3 3
8 3
14 3
Output
1 1 1
4 2 2
2 6 6


-----Note-----

None