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>
using namespace std;
int main() {
  long long int l, r, k;
  cin >> l >> r >> k;
  if (k == 1 || l == r || (r - l == 1 && l % 2 && (l ^ r) >= l)) {
    cout << l << "\n1\n" << l << endl;
    return 0;
  }
  long long int num = 1, ind;
  for (int i = 0;; i++) {
    if (num > l) {
      ind = i;
      break;
    }
    num *= 2;
  }
  if (num + num / 2 <= r && k >= 3) {
    cout << "0\n3\n"
         << num - 1 << " " << num + num / 2 << " " << num + num / 2 - 1 << endl;
    return 0;
  }
  if (r - l == 1) {
    cout << (l ^ (l + 1)) << "\n2\n" << l << " " << l + 1 << endl;
    return 0;
  }
  if (l % 2) l++;
  if (l + 3 <= r && k >= 4) {
    cout << "0\n4\n"
         << l << " " << l + 1 << " " << l + 2 << " " << l + 3 << endl;
  } else {
    cout << "1\n2\n" << l << " " << l + 1 << endl;
  }
  return 0;
}