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, i, x, p, v;
  cin >> l >> r >> k;
  vector<long long> ans;
  if (l == r || k == 1) {
    ans.push_back(l);
  } else {
    x = l + (l & 1);
    if (x + 3 <= r && k >= 4) {
      for (i = 0; i <= 3; ++i) ans.push_back(x + i);
    } else {
      p = 1;
      while (p <= l) p <<= 1;
      p |= p >> 1;
      if (p <= r && (l ^ p) <= r && k >= 3) {
        ans.push_back(l);
        ans.push_back(l ^ p);
        ans.push_back(p);
      } else if (x + 1 <= r) {
        ans.push_back(x);
        ans.push_back(x + 1);
      } else {
        ans.push_back(l);
        if ((l ^ (l + 1)) <= l) ans.push_back(l + 1);
      }
    }
  }
  v = ans[0];
  for (i = 1; i < ans.size(); ++i) v ^= ans[i];
  cout << v << ' ' << ans.size() << ' ';
  for (i = 0; i < ans.size(); ++i) cout << ans[i] << ' ';
}