Not only STL

As you know in STL there is a function called next_permutation, when you send a array to it, it will Rearranges the elements in the array into the next lexicographically greater permutation.

But today we need a next_k_permutation, you may say we can just apply k times next_permutation function to the array. Yes, you are right, but when k is very large it is not efficient enough.

So you are expected to write a program when given an array and k to find its next_k_permutation.
Note the next permutation of the permutation with largest dictionary order is the permutation with the minimum dictionary order. For example next permutation of (3,2,1) is (1,2,3).

Multi test cases(about 1000). Each case contains two lines. The first line contains two integers n which indicates the length of the permutation and k. The second line contains n integers $a_1, a_2, a_3, \ldots, a_n$ Process to the end of file.
$1 \leq n \leq 2000$
$1 \leq k \leq 10^{12}$
$1 \leq a_i \leq 2000$

For each case, output the answer in a single line.

3 1
1 2 3
3 1
1 1 2

1 3 2
1 2 1

BestCoder Round #12