permutation 1

Problem Description

A sequence of length $n$ is called a permutation if and only if it's composed of the first $n$ positive integers and each number appears exactly once. Here we define the "difference sequence" of a permutation $p_1, p_2, \ldots, p_n$ as $p_2 - p_1, p_3 - p_2, \ldots, p_n - p_{n-1}$. In other words, the length of the difference sequence is $n-1$ and the $i$-th term is $p_{i+1}-p_i$ Now, you are given two integers $N, K$. Please find the permutation with length $N$ such that the difference sequence of which is the $K$-th lexicographically smallest among all difference sequences of all permutations of length $N$.

Input

The first line contains one integer $T$ indicating that there are $T$ tests. Each test consists of two integers $N, K$ in a single line.

• $1 \le T \le 40$
• $2 \le N \le 20$
• $1 \le K \le \min(10^4,N!)$

Output

For each test, please output $N$ integers in a single line. Those $N$ integers represent a permutation of $1$ to $N$, and its difference sequence is the $K$-th lexicographically smallest.

Sample Input

7

3 1

3 2

3 3

3 4

3 5

3 6

20 10000

Sample Output

3 1 2

3 2 1

2 1 3

2 3 1

1 2 3

1 3 2

20 1 2 3 4 5 6 7 8 9 10 11 13 19 18 14 16 15 17 12

Source

2019 Multi-University Training Contest 5