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.

Input

The first line contains three space-separated integers $*l*, *r*, *k*$ $(1 ≤ *l* ≤ *r* ≤ 10^{12}; 1 ≤ *k* ≤ *min*(10^{6}, *r* - *l* + 1))$.

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