Let $p(n,k)$ denote the $k$ th permutation (in lexicographical order) of $1 \dots n$ . For example, $p(4,1)=[1,2,3,4]$ and $p(4,2)=[1,2,4,3]$ .
Your task is to process two types of tests:
Givennandk, findp(n,k)Givennandp(n,k), findk
The first line has an integer $t$ : the number of tests.
Each test is either "1 $n$ $k$ " or "2 $n$ $p(n,k)$ ".
For each test, print the answer according to the example.
6 1 4 1 1 4 2 2 4 1 2 3 4 2 4 1 2 4 3 1 5 42 2 5 2 4 5 3 1\n · · \n · · \n · · · · · \n · · · · · \n · · \n · · · · · · \n
1 2 3 4 1 2 4 3 1 2 2 4 5 3 1 42· · · \n · · · \n \n \n · · · · \n \n