# SUM Equals LCM

Amra shobai Raja
Limits 1s, 512 MB

Given $N$, print a sequence of $N$ positive integers $A_1, A_2, \ldots, A_N$ that satisfy the following conditions:

• $\sum_{i=1}^{N}A_i = \text{lcm}(A_1, A_2, \ldots, A_N)$
• $1 \leq A_i \leq 10^9$

If there exists no such sequence, print $-1$.

• lcm denotes the least common multiple. The least common multiple of some positive integers is the least positive integer which is multiple for each of them.

## Input

The first line of each test case contains an integer $T(1 \leq T \leq 100)$— the number of test cases.

Each of the next $T$ lines will contain an integer $N(1 \leq N \leq 10^5)$— the length of the sequence.

Sum of $N$ over all test cases does not exceed $10^6$.

## Output

For each test case, print $N$ space separated positive integers that satisfy the given conditions on a separate line. If there exists no such sequence, print $-1$.

If there are multiple sequences that satisfy the conditions, you can output any of them.

## Sample

InputOutput
3
1
2
4

1
-1
2 3 3 4