Construct An Array

 Given an integer 

N$N$, construct an array A$A$ of length N$N$ such that:

• 1≤Ai≤1018$1\le A_i\le {10}^{18}$ for all (1≤i≤N)$(1\le i\le N)$;
• There exists a subsequence of length greater than 1$1$ such that the gcd of all elements of the subsequence is i$i$, for all 1≤i≤N$1\le i\le N$.
  More formally, for all (1≤i≤N)$(1\le i\le N)$, there exists a subsequence S$S$ of array A$A$ such that the length of the subsequence is k(2≤k≤N)$k(2\le k\le N)$ and gcd(S1,S2,…,Sk)=i$gcd(S_1,S_2,\dots ,S_k)=i$.

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

Input Format

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

Output Format

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

If there exist multiple such arrays, print any.

Constraints

• 1≤T≤103$1\le T\le {10}^3$
• 3≤N≤103$3\le N\le {10}^3$
• Sum of N$N$ over all test cases does not exceed 5⋅103$5\cdot {10}^3$.

Sample Input 1 

2
3
4

Sample Output 1 

2 3 6
4 24 10 15

Explanation

Test case 1$1$: A possible array satisfying all the conditions is [2, 3, 6]:

• For i=1$i=1$: Choose S=[A1,A2,A3]=[2,3,6]$S=[A_1,A_2,A_3]=[2,3,6]$. Thus, gcd(2,3,6)=1$gcd(2,3,6)=1$.
• For i=2$i=2$: Choose S=[A1,A3]=[2,6]$S=[A_1,A_3]=[2,6]$. Thus, gcd(2,6)=2$gcd(2,6)=2$.
• For i=3$i=3$: Choose S=[A2,A3]=[3,6]$S=[A_2,A_3]=[3,6]$. Thus, gcd(3,6)=3$gcd(3,6)=3$.

Test case 2$2$: A possible array satisfying all the conditions is [4, 24, 10, 15]:

• For i=1$i=1$: Choose S=[4,24,10,15]$S=[4,24,10,15]$. Thus, gcd(4,24,10,15)=1$gcd(4,24,10,15)=1$.
• For i=2$i=2$: Choose S=[24,10]$S=[24,10]$. Thus, gcd(24,10)=2$gcd(24,10)=2$.
• For i=3$i=3$: Choose S=[24,15]$S=[24,15]$. Thus, gcd(24,15)=3$gcd(24,15)=3$.
• For i=4$i=4$: Choose S=[4,24]$S=[4,24]$. Thus, gcd(4,24)=4$gcd(4,24)=4$