Little Victor adores the sets theory. Let us remind you that a set is a group of numbers where all numbers are pairwise distinct. Today Victor wants to find a set of integers S that has the following properties:

• for all x the following inequality holds l ≤ x ≤ r;
• 1 ≤ |S| ≤ k;
• lets denote the i-th element of the set S as s_i; value must be as small as possible.

Help Victor find the described set.

The first line contains three space-separated integers l, r, k (1 ≤ l ≤ r ≤ 10¹²; 1 ≤ k ≤ min(10⁶, r - l + 1)).

Print the minimum possible value of f(S). Then print the cardinality of set |S|. Then print the elements of the set in any order.

If there are multiple optimal sets, you can print any of them.