CF460D.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 s__i; value must be as small as possible.

Help Victor find the described set.

小维克多非常喜爱集合论。我们来回顾一下：集合是一组两两互不相同的数。今天，维克多希望找到一个整数集合 $ S $，使其满足以下性质：

• 对所有 $ x \in S $，均满足不等式 $ l \leq x \leq r $；
• $ 1 \leq |S| \leq k $；
• 记集合 $ S $ 的第 $ i $ 个元素为 $ s_i $；则表达式 $ \sum_{i=1}^{|S|} \sum_{j=i}^{|S|} (s_j - s_i) $ 的值应尽可能小。

请帮助维克多找出满足上述条件的集合。

The first line contains three space-separated integers l, r, k (1 ≤ l ≤ r ≤ 1012; 1 ≤ k ≤ min(106, r - l + 1)).

第一行包含三个以空格分隔的整数 $l$、$r$、$k$（$1 \leq l \leq r \leq 10^{12}$；$1 \leq k \leq \min(10^6, r - l + 1)$）。

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.

输出函数 $f(S)$ 的最小可能值。然后输出集合 $|S|$ 的基数（即元素个数）。最后以任意顺序输出该集合的各个元素。

如果存在多个最优集合，你可以输出其中任意一个。

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

运算符 表示按位异或运算，即 XOR 运算。