D. Inversion Value of a Permutation
time limit per test
3 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

A permutation of length $$$n$$$ is an array of $$$n$$$ integers, where each number from $$$1$$$ to $$$n$$$ appears exactly once. An inversion in a permutation $$$p$$$ is a pair of indices $$$(i, j)$$$ such that $$$i \lt j$$$ and $$$p_i \gt p_j$$$.

For a permutation $$$p$$$, we define its inversion value as the number of its subsegments that contain at least one inversion. Formally, this is the number of pairs of integers $$$(l, r)$$$ ($$$1 \le l \lt r \le n$$$) for which there exists a pair of indices $$$(i, j)$$$ satisfying the following conditions: $$$l \le i \lt j \le r$$$ and $$$p_i \gt p_j$$$.

For example, for the permutation $$$[3, 1, 4, 2]$$$, the inversion value is $$$5$$$.

You are given two integers $$$n$$$ and $$$k$$$. Your task is to construct a permutation of length $$$n$$$ with an inversion value equal to exactly $$$k$$$.

Input

The first line contains one integer $$$t$$$ ($$$1 \le t \le 500$$$) — the number of test cases.

Each test case consists of a single line containing two integers $$$n$$$ and $$$k$$$ ($$$2 \le n \le 30$$$; $$$0 \le k \le \dfrac{n(n-1)}{2}$$$).

Output

For each test case, output the answer as follows:

  • if the desired permutation does not exist, output a single integer $$$0$$$;
  • otherwise, output $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ — the desired permutation. If there are multiple such permutations, you may output any of them.
Example
Input
5
4 5
5 10
5 0
6 8
3 1
Output
3 1 4 2
5 4 3 2 1
1 2 3 4 5
2 3 5 6 1 4
0