Given an integer N, construct an array A of length N such that:
1 ≤ A_{i} ≤ 10^{18} for all (1 ≤ i ≤ N);
There exists a [subsequence] of length greater than 1 such that the [gcd] of all elements of the subsequence is i, for all 1 ≤ i ≤ N.
More formally, for all (1 ≤ i ≤ N), there exists a subsequence S of array A such that the length of the subsequence is k (2 ≤ k ≤ N) and $gcd(S_{1},S_{2},\ldots,S_{k})=i$.

It can be proven that it is always possible to construct such A under given constraints. If there exist multiple such arrays, print any.

------ Input Format ------

• The first line of input contains a single integer T, denoting the number of test cases. The description of T test cases follow.
• The only line of each test case contains an integer N - the length of the array to be constructed.

------ Output Format ------

For each test case, output a single line containing N space-separated integers, denoting the elements of the array A. The i^{th} of these N integers is the i^{th} element of the array A.

If there exist multiple such arrays, print any.

------ Constraints ------

$1 ≤ T ≤ 10^{3}$
$3 ≤ N ≤ 10^{3}$
- Sum of $N$ over all test cases does not exceed $5 \cdot 10^{3}$.

----- Sample Input 1 ------
2
3
4

----- Sample Output 1 ------
2 3 6
4 24 10 15
----- explanation 1 ------
Test case $1$: A possible array satisfying all the conditions is [2, 3, 6]:
- For $i=1$: Choose $S = [A_{1}, A_{2}, A_{3}] = [2, 3, 6]$. Thus, $gcd(2,3,6)=1$.
- For $i=2$: Choose $S = [A_{1}, A_{3}] = [2, 6]$. Thus, $gcd(2,6)=2$.
- For $i=3$: Choose $S = [A_{2}, A_{3}] = [3, 6]$. Thus, $gcd(3,6)=3$.

Test case $2$: A possible array satisfying all the conditions is [4, 24, 10, 15]:
- For $i=1$: Choose $S = [4, 24, 10, 15]$. Thus, $gcd(4,24,10,15)=1$.
- For $i=2$: Choose $S = [24, 10]$. Thus, $gcd(24,10)=2$.
- For $i=3$: Choose $S = [24, 15]$. Thus, $gcd(24,15)=3$.
- For $i=4$: Choose $S = [4, 24]$. Thus, $gcd(4,24)=4$.

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