D. Little Victor and Set
time limit per test
1 second
memory limit per test
256 megabytes
input
stdin
output
stdout

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.

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.

Examples
Input
8 15 3
Output
1
2
10 11
Input
8 30 7
Output
0
5
14 9 28 11 16
Note

Operation represents the operation of bitwise exclusive OR. In other words, it is the XOR operation.