Yet another subarray problem

 Given a positive integer 

N$N$, find an array A=[A1,A2,…,AN]$A=[A_1,A_2,\dots ,A_N]$ of length N$N$ consisting of distinct integers from 1$1$ to 109${10}^9$, such that the following condition is satisfied for each subarray [AL,AL+1,…,Ar]$[A_L,A_{L+1},\dots ,A_r]$ (1≤L≤R≤N$1\le L\le R\le N$):

• The sum of elements in the subarray is divisible by its length i.e. AL+AL+1+…+AR$A_L+A_{L+1}+\dots +A_R$ is divisible by R−L+1$R-L+1$.

It can be proved that such an array always exists under given constraints.

If there are multiple possible arrays, you may print any of them.

Input Format

• The first line of the input contains a single integer T$T$, denoting the number of test cases. The description of T$T$ test cases follows.
• Each test case consists of a single line containing one positive integer N$N$, the length of the array A$A$.

Output Format

For each test case, print one line containing N$N$ space-separated integers, the contents of the array A$A$.

Constraints

• 1≤T≤100$1\le T\le 100$
• 1≤N≤1000$1\le N\le 1000$
• Sum of N$N$ over all test cases doesn't exceed 5000$5000$

Sample Input 1 

3
1
2
3

Sample Output 1 

1
1 3
4 2 6

Explanation

Test case 1$1$:

For array A=[1]$A=[1]$,

• The sum of elements of the subarray [1]$[1]$ is equal to 1$1$ which is divisible by 1$1$, the length of this subarray.

Test case 2$2$:

For array A=[1,3]$A=[1,3]$,

• The sum of elements of the subarray [1]$[1]$ is equal to 1$1$ which is divisible by 1$1$, the length of this subarray.
• The sum of elements of the subarray [3]$[3]$ is equal to 3$3$ which is divisible by 1$1$, the length of this subarray.
• The sum of elements of the subarray [1,3]$[1,3]$ is equal to 4$4$ which is divisible by 2$2$, the length of this subarray.

Test case 3$3$:

For array A=[4,2,6]$A=[4,2,6]$,

• The sum of elements of the subarray [4]$[4]$ is equal to 4$4$ which is divisible by 1$1$, the length of this subarray.
• The sum of elements of the subarray [2]$[2]$ is equal to 2$2$ which is divisible by 1$1$, the length of this subarray.
• The sum of elements of the subarray [6]$[6]$ is equal to 6$6$ which is divisible by 1$1$, the length of this subarray.
• The sum of elements of the subarray [4,2]$[4,2]$ is equal to 6$6$ which is divisible by 2$2$, the length of this subarray.
• The sum of elements of the subarray [2,6]$[2,6]$ is equal to 8$8$ which is divisible by 2$2$, the length of this subarray.
• The sum of elements of the subarray [4,2,6]$[4,2,6]$ is equal to 12$12$ which is divisible by 3$3$, the length of this subarray.

Problem Code: SUBPRB