Picking Out Numbers

Seonggwan wants to build a set $S$ that satisfies all of the following conditions.

• Every element of $S$ is a natural number, and no two elements are equal.
• Every element of $S$ is at least $l$ and at most $r$.
• The number of elements of $S$ is at least $1$ and at most $k$.

Choose $S$ so that the bitwise XOR of all its elements is as small as possible, and find that XOR value.

The first line contains the natural numbers $l$, $r$, $k$, separated by spaces. ($1 \le l \le r \le 10^{12}$, $1 \le k \le \min(10^6, r-l+1)$)

Print the smallest XOR value on the first line. Several sets can reach that smallest value, but the output is that single value.