K-th Permutation with Given Inversion Count

Given three natural numbers n, k, and x, find the k-th smallest permutation in lexicographical order among all permutations of the set {1, 2, ..., n} that have exactly x inversion pairs. An inversion pair is defined as a pair of indices (i, j) such that i < j and a_i > a_j. It is guaranteed that such a permutation exists.

Note:

• Comparisons between permutations are done in lexicographical order.
• The permutation is a rearrangement of 1 through n.
• The k-th smallest is counted starting from 1.

inputFormat

The input consists of a single line containing three integers n, k, and x separated by spaces.

Constraints: n is a natural number, and 0 ≤ x ≤ n*(n-1)/2. It is guaranteed that there exists at least one permutation of {1,2,…,n} with exactly x inversions, and that the k-th such permutation exists.

outputFormat

Output the required permutation as a sequence of n space-separated integers in one line.

sample

3 1 1

1 3 2