# Codeforces 460D. 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 lxr;
• 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 ≤ lr ≤ 1012; 1 ≤ kmin(106, rl + 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.

### 分析

• 如果 $k=1$，显然选择 $l$ 最优；
• 如果 $k\ge 2$，因为区间较大，必然可以选出相邻的两个数使其异或和为 $1$；
• 如果 $k\ge 4$，因为区间较大，必然可以选出两组异或和为 $1$ 的数对，四个数的异或和就为 $0$。