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 $\text{[math]}$ the following inequality holds l ≤ x ≤ r;
1 ≤ |S| ≤ k;
lets denote the i-th element of the set S as s_i; value $\text{[math]}$ 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.

Note

Operation $\text{[math]}$ represents the operation of bitwise exclusive OR. In other words, it is the XOR operation.

Little Victor and Set

Examples