17995번 - Fixed Point Permutations 다국어

문제

A permutation of size n is a list of integers (p₁, p₂, ..., p_n) from 1 to n such that each number appears exactly once.

The number of fixed points of a permutation is the number of indices i such that p_i = i.

Given three numbers n, m, and k, find the k^th lexicographically smallest permutation of size n that has exactly m fixed points (or print -1 if there are fewer than k permutations that satisfy the condition).

입력

The single line of input contains three space-separated integers

n (1 ≤ n ≤ 50) m (0 ≤ m ≤ n) k (1 ≤ k ≤ 10¹⁸)

where n is the size of the permutations, m is the number of desired fixed points, and the output should be the k^th lexicographically smallest permutation of the numbers 1 to n that has exactly m fixed points.

출력

Output the desired permutation on a single line as a sequence of n space-separated integers, or output -1 if no such permutation exists.

제한

힌트