Problem: 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 <image> the following inequality holds l ≤ x ≤ r; 
  * 1 ≤ |S| ≤ k; 
  * lets denote the i-th element of the set S as si; value <image> 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.

Examples

Input

8 15 3


Output

1
2
10 11


Input

8 30 7


Output

0
5
14 9 28 11 16

Note

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

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
struct lemur {
  long long value;
  std::vector<long long> answer;
  lemur(void) : value(), answer() {}
  lemur(const std::vector<long long>& a) : value(0), answer(a) {
    for (auto& x : answer) {
      value ^= x;
    }
  }
  bool operator<(const lemur& l) const { return value < l.value; }
  void print(void) {
    std::cout << value << "\n" << answer.size() << "\n";
    for (auto& x : answer) {
      std::cout << x << " ";
    }
    std::cout << "\n";
  }
};
int main(void) {
  lemur best;
  long long lg, l, r, k, w, x, y, z;
  std::cin >> l >> r >> k;
  w = r - l + 1;
  best = lemur({l});
  if (k >= 2) {
    best = std::min(lemur({l, l + 1}), best);
    if (w > 2) {
      best = std::min(lemur({l + 1, l + 2}), best);
    }
  }
  if (k >= 3) {
    x = l;
    for (lg = 1; lg <= x; lg <<= 1)
      ;
    z = lg | (lg >> 1);
    y = lg | (x ^ (lg >> 1));
    if (z <= r) {
      best = std::min(lemur({x, y, z}), best);
      z = lg | (lg << 1);
      while (z <= r) {
        x = lg;
        y = lg << 1;
        best = std::min(lemur({x, y, z}), best);
        lg <<= 1;
        z = lg | (lg << 1);
      }
    }
  }
  if (k >= 4) {
    best = std::min(lemur({l, l + 1, l + 2, l + 3}), best);
    if (w > 4) {
      best = std::min(lemur({l + 1, l + 2, l + 3, l + 4}), best);
    }
  }
  best.print();
  return 0;
}