C. Yet Another Permutation Problem(Codeforces Round 893 (Div. 2))

Alex got a new game called “GCD permutations” as a birthday present. Each round of this game proceeds as follows:

• First, Alex chooses a permutation${}^{†}$ $a_1,a_2,\dots ,a_n$ of integers from $1$ to $n$.
• Then, for each $i$ from $1$ to $n$, an integer $d_i=\gcd (a_i,a_{(i\mathrm{mod}n)+1})$ is calculated.
• The score of the round is the number of distinct numbers among $d_1,d_2,\dots ,d_n$.

Alex has already played several rounds so he decided to find a permutation $a_1,a_2,\dots ,a_n$ such that its score is as large as possible.

Recall that $\gcd (x,y)$ denotes the greatest common divisor (GCD) of numbers $x$ and $y$, and $x\mathrm{mod}y$ denotes the remainder of dividing $x$ by $y$.

${}^{†}$A permutation of length $n$ is an array consisting of $n$ distinct integers from $1$ to $n$ in arbitrary order. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation ($2$ appears twice in the array), and $[1,3,4]$ is also not a permutation ($n=3$ but there is $4$ in the array).

Input

The first line of the input contains a single integer $t$ ($1\le t\le 10^4$) — the number of test cases.

Each test case consists of one line containing a single integer $n$ ($2\le n\le 10^5$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$.

Output

For each test case print $n$ distinct integers $a_1,a_2,\dots ,a_n$ ($1\le a_i\le n$) — the permutation with the largest possible score.

If there are several permutations with the maximum possible score, you can print any one of them.

Example

input
4
5
2
7
10
output
1 2 4 3 5
1 2
1 2 3 6 4 5 7
1 2 3 4 8 5 10 6 9 7

Note

In the first test case, Alex wants to find a permutation of integers from $1$ to $5$. For the permutation $a=[1,2,4,3,5]$, the array $d$ is equal to $[1,2,1,1,1]$. It contains $2$ distinct integers. It can be shown that there is no permutation of length $5$ with a higher score.

In the second test case, Alex wants to find a permutation of integers from $1$ to $2$. There are only two such permutations: $a=[1,2]$ and $a=[2,1]$. In both cases, the array $d$ is equal to $[1,1]$, so both permutations are correct.

In the third test case, Alex wants to find a permutation of integers from $1$ to $7$. For the permutation $a=[1,2,3,6,4,5,7]$, the array $d$ is equal to $[1,1,3,2,1,1,1]$. It contains $3$ distinct integers so its score is equal to $3$. It can be shown that there is no permutation of integers from $1$ to $7$ with a score higher than $3$.

解题思路

给一个整数n，需要用1到n这n个数字组成一个整数数组a，再用a数组每相邻两个数的最大公约数组成一个新数组b（最后一个与第一个组），使b中的不同数字数量最多。

代码实现

#include
#include

using namespace std;

int main() {
    int t;
    cin >> t;
    while (t--) {
        int n;
        cin >> n;
        vector<int> a(n);
        int cur = 0;
        for (int i = 1; i <= n; i += 2) {
            for (int j = i; j <= n; j *= 2) {
                a[cur++] = j;
            }
        }
        for (int i = 0; i<n; ++i) {
            cout << a[i] << " ";
        }
        cout << '\n';
    }
    return 0;
}