D. Inversion Value of a Permutation

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<𝑗

 and 𝑝

𝑖

>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≤𝑙<𝑟≤𝑛

) for which there exists a pair of indices (𝑖,𝑗)

 satisfying the following conditions: 𝑙≤𝑖<𝑗≤𝑟

 and 𝑝

𝑖

>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≤𝑡≤500

) — the number of test cases.

Each test case consists of a single line containing two integers 𝑛

 and 𝑘

 (2≤𝑛≤30

; 0≤𝑘≤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

Copy

5
4 5
5 10
5 0
6 8
3 1

Output

Copy

3 1 4 2
5 4 3 2 1
1 2 3 4 5
2 3 5 6 1 4
0