Gorilla and Noobish_Monk found three numbers $$$n$$$, $$$m$$$, and $$$k$$$ ($$$m \lt k$$$). They decided to construct a permutation$$$^{\dagger}$$$ of length $$$n$$$.

For the permutation, Noobish_Monk came up with the following function: $$$g(i)$$$ is the sum of all the numbers in the permutation on a prefix of length $$$i$$$ that are not greater than $$$m$$$. Similarly, Gorilla came up with the function $$$f$$$, where $$$f(i)$$$ is the sum of all the numbers in the permutation on a prefix of length $$$i$$$ that are not less than $$$k$$$. A prefix of length $$$i$$$ is a subarray consisting of the first $$$i$$$ elements of the original array.

For example, if $$$n = 5$$$, $$$m = 2$$$, $$$k = 5$$$, and the permutation is $$$[5, 3, 4, 1, 2]$$$, then:

$$$f(1) = 5$$$, because $$$5 \ge 5$$$; $$$g(1) = 0$$$, because $$$5 \gt 2$$$;
$$$f(2) = 5$$$, because $$$3 \lt 5$$$; $$$g(2) = 0$$$, because $$$3 \gt 2$$$;
$$$f(3) = 5$$$, because $$$4 \lt 5$$$; $$$g(3) = 0$$$, because $$$4 \gt 2$$$;
$$$f(4) = 5$$$, because $$$1 \lt 5$$$; $$$g(4) = 1$$$, because $$$1 \le 2$$$;
$$$f(5) = 5$$$, because $$$2 \lt 5$$$; $$$g(5) = 1 + 2 = 3$$$, because $$$2 \le 2$$$.

Help them find a permutation for which the value of $$$\left(\sum_{i=1}^n f(i) - \sum_{i=1}^n g(i)\right)$$$ is maximized.

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

Input

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

The only line of each case contains three integers $$$n$$$, $$$m$$$, $$$k$$$ ($$$2\le n \le 10^5$$$; $$$1 \le m \lt k \le n$$$) — the size of the permutation to be constructed and two integers.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output the permutation — a set of numbers that satisfies the conditions of the problem. If there are multiple solutions, output any of them.

Note

In the first example, $$$\left(\sum_{i=1}^n f(i) - \sum_{i=1}^n g(i)\right) = 5 \cdot 5 - (0 \cdot 3 + 1 + 3) = 25 - 4 = 21$$$

Gorilla and Permutation

Examples