D. Constructing the Arraytime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an array a of length n consisting of zeros. You perform n actions with this array: during the i-th action, the following sequence of operations appears:  Choose the maximum by length subarray (continuous subsegment) consisting only of zeros, among all such segments choose the leftmost one;  Let this segment be [l; r]. If r-l+1 is odd (not divisible by 2) then assign (set) a[\frac{l+r}{2}] := i (where i is the number of the current action), otherwise (if r-l+1 is even) assign (set) a[\frac{l+r-1}{2}] := i. Consider the array a of length 5 (initially a=[0, 0, 0, 0, 0]). Then it changes as follows:  Firstly, we choose the segment [1; 5] and assign a[3] := 1, so a becomes [0, 0, 1, 0, 0];  then we choose the segment [1; 2] and assign a[1] := 2, so a becomes [2, 0, 1, 0, 0];  then we choose the segment [4; 5] and assign a[4] := 3, so a becomes [2, 0, 1, 3, 0];  then we choose the segment [2; 2] and assign a[2] := 4, so a becomes [2, 4, 1, 3, 0];  and at last we choose the segment [5; 5] and assign a[5] := 5, so a becomes [2, 4, 1, 3, 5]. Your task is to find the array a of length n after performing all n actions. Note that the answer exists and unique.You have to answer t independent test cases.InputThe first line of the input contains one integer t (1 \le t \le 10^4) — the number of test cases. Then t test cases follow.The only line of the test case contains one integer n (1 \le n \le 2 \cdot 10^5) — the length of a.It is guaranteed that the sum of n over all test cases does not exceed 2 \cdot 10^5 (\sum n \le 2 \cdot 10^5).OutputFor each test case, print the answer — the array a of length n after performing n actions described in the problem statement. Note that the answer exists and unique.ExampleInput
6
1
2
3
4
5
6
Output
1 
1 2 
2 1 3 
3 1 2 4 
2 4 1 3 5 
3 4 1 5 2 6 

6
1
2
3
4
5
6

1  1 2  2 1 3  3 1 2 4  2 4 1 3 5  3 4 1 5 2 6  
['constructive algorithms', 'data structures', 'sortings', '*1600']