Bad Tree

Binary search trees speed up searches only when the height of the tree is much smaller than the number of values stored in it. Judges, however, try to build worst case data. So in binary search tree problems, the judges almost always create data where $n$ nodes are inserted in a particular order that makes the tree height the worst possible, $n-1$.

Without loss of generality, let the $n$ values to insert be 1, 2, 3, ..., n. For $n=5$, inserting the values in the order 5, 1, 4, 3, 2 gives a binary search tree of height 4.

Many permutations of the integers 1 through $n$ produce a tree of height $n-1$ when inserted in that order. Write a program that finds the $k$th permutation in lexicographical order among them.

The input is a single line with two space-separated integers $n$ ($1 \le n \le 100$) and $k$ ($1 \le k \le 10^{18}$). $n$ is the number of nodes, and $k$ is the position of the wanted permutation in lexicographical order.

Print the $k$th permutation of the integers 1 through $n$ that, when inserted into a binary search tree in that order, produces a tree of height $n-1$. Print the numbers on one line, with a space after each number. If no such permutation exists, print -1.