Even and Odd Combinations

Let a $k$-combination out of $n$ be a $k$-element subset of the $n$-element set $\\{1, 2, \ldots, n\\}$. To denote a combination, list its elements in ascending order. For example, $2$-combinations out of $3$ look as follows: $\\{1, 2\\}$, $\\{1, 3\\}$, $\\{2, 3\\}$.

Let a combination be even if the number of its elements is an even number, and odd otherwise. For a fixed $n > 0$, consider two sets: $A\_n$, the set of all even combinations out of $n$, and $B\_n$, the set of all odd combinations out of $n$. It can be shown that $A\_n$ and $B\_n$ contain the same number of combinations.

For each $n = 1, 2, \ldots, 50$, your task is as follows. Construct any bijection (a one-to-one correspondence) between the sets $A\_n$ and $B\_n$. After that, given an element of one of these sets, print the corresponding element of the other set.