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 l, r, k, f;
  while (cin >> l >> r >> k) {
    f = 1;
    if (k >= 4)
      for (long long i = l; i + 2 < r && f; i++)
        if (i % 2 == 0) {
          cout << 0 << endl
               << 4 << endl
               << i << " " << i + 1 << " " << i + 2 << " " << i + 3 << endl;
          f = 0;
        }
    if (!f) continue;
    if (k >= 3) {
      long long bit = 3, now = l;
      while (now > 1) {
        now >>= 1;
        bit <<= 1;
      }
      if (bit <= r) {
        cout << 0 << endl
             << 3 << endl
             << bit << " " << (bit ^ l) << " " << l << endl;
        continue;
      }
    }
    if (k >= 2) {
      if (l % 2 == 0) {
        cout << 1 << endl << 2 << endl << l << " " << l + 1 << endl;
        continue;
      }
      if (l % 2 == 1 && l + 2 <= r) {
        cout << 1 << endl << 2 << endl << l + 1 << " " << l + 2 << endl;
        continue;
      }
      if ((l ^ r) < l) {
        cout << (l ^ r) << endl << 2 << endl << l << " " << r;
        continue;
      }
    }
    cout << l << endl << 1 << endl << l << endl;
  }
  return 0;
}