Little Victor and Set
Description
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 si; 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.
Input
The first line contains three space-separated integers l, r, k (1 ≤ l ≤ r ≤ 1012; 1 ≤ k ≤ min(106, r - l + 1)).
Output
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.
Samples
8 15 3
1
2
10 11
8 30 7
0
5
14 9 28 11 16
Note
Operation 
represents the operation of bitwise exclusive OR. In other words, it is the XOR operation.