Even and Odd Combinations

A $k$-combination out of $n$ is 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, the 2-combinations out of 3 are $\{1, 2\}$, $\{1, 3\}$, and $\{2, 3\}$.

A combination is even if it has an even number of elements, and odd otherwise. For a fixed $n > 0$, let $A_n$ be the set of all even combinations out of $n$, and let $B_n$ be 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 $n = 1, 2, \ldots, 50$, do the following. Construct any bijection between $A_n$ and $B_n$. Then, given an element of one of these sets, print the corresponding element of the other set.