Little Victor and Set

题意翻译

给定一个区间l,r与一个数k。 在l~r中找不超过k个数（不能重复选），使得这些数的异或和最小，输出任意方案。

题目描述

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.

输入输出格式

输入格式

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

输出格式

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.

输入输出样例

输入样例 #1

8 15 3

输出样例 #1

1
2
10 11

输入样例 #2

8 30 7

输出样例 #2

0
5
14 9 28 11 16

说明

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