#D7353. Little Victor and Set
Little Victor and Set
Little Victor and Set
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.
inputFormat
Input
The first line contains three space-separated integers l, r, k (1 ≤ l ≤ r ≤ 1012; 1 ≤ k ≤ min(106, r - l + 1)).
outputFormat
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.
样例
8 30 7
0
4
8 9 10 11