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>
#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
using namespace std;
long long l, r, k;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> l >> r >> k;
  if (k >= 4) {
    if (r - l >= 4 || (r - l == 3 && l % 2 == 0)) {
      cout << "0\n4\n";
      if (l % 2 == 1) l++;
      for (long long i = 0; i <= 3; i++) {
        cout << l + i << " ";
      }
      return 0;
    }
  }
  if (k >= 3) {
    long long luu = 0;
    for (long long i = 40; i >= 0; i--) {
      if ((l >> i) & 1) {
        luu = i;
        break;
      }
    }
    long long hi = (1LL << luu) | (1LL << (luu + 1));
    if (hi <= r) {
      cout << "0\n3\n";
      cout << l << " " << (l ^ hi) << " " << hi;
      return 0;
    }
  }
  if (k >= 2) {
    if (r - l >= 2 || (r - l == 1 && l % 2 == 0)) {
      cout << "1\n2\n";
      if (l % 2 == 1) l++;
      cout << l << " " << l + 1;
      return 0;
    }
    if (r - l == 1 && (r ^ l) < l) {
      cout << (r ^ l) << "\n";
      cout << 2 << "\n";
      cout << l << " " << r << "\n";
      return 0;
    }
  }
  if (k >= 1) {
    cout << l << '\n' << 1 << "\n" << l;
  }
  return 0;
}