Permutation Order

There are N! permutations made by using each integer from 1 through N exactly once.

Permutations are ordered lexicographically. Compare two permutations from left to right; at the first position where they differ, the permutation with the smaller number comes earlier. For N=3, the order is {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {3, 2, 1}.

Given N, perform one of two tasks. Task 1 asks for the k-th permutation. Task 2 asks for the 1-based position of a given permutation.

The first line contains an integer N (1 <= N <= 20).

The first integer on the second line is the task number. If it is 1, it is followed by an integer k (1 <= k <= N!). If it is 2, it is followed by N integers forming a permutation of 1 through N.

For task 1, output the N integers of the k-th permutation separated by spaces. For task 2, output the 1-based lexicographic position of the given permutation.