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;
  cin >> l >> r >> k;
  if (k > 4 || (k == 4 && (r - l > 3 || l % 2 == 0))) {
    cout << 0 << endl;
    cout << 4 << endl;
    if (l % 2 == 1) l++;
    for (i = l; i < l + 4; i++) cout << i << " ";
    return 0;
  }
  if (k >= 3 && l == 1) {
    cout << 0 << endl;
    cout << 3 << endl;
    for (i = l; i < l + 3; i++) cout << i << " ";
    return 0;
  }
  if (k >= 3) {
    long long j = 1, z, f;
    while (j <= l) j <<= 1;
    j = j + j / 2;
    z = j ^ l;
    if (j <= r) {
      cout << "0\n";
      cout << "3\n";
      cout << j << " " << z << " " << l;
      return 0;
    }
  }
  if (k == 1) {
    cout << l << endl;
    cout << 1 << endl;
    cout << l;
    return 0;
  }
  if (k >= 2 && (r - l > 1 || l % 2 == 0)) {
    cout << 1 << endl;
    cout << 2 << endl;
    if (l % 2 == 1) l++;
    cout << l << " " << l + 1;
    return 0;
  }
  if (k >= 2 && (r - l == 1 && l % 2 == 1)) {
    long long a = l ^ r;
    if (a <= l) {
      cout << a << endl;
      cout << 2 << endl;
      cout << l << " " << l + 1;
    } else {
      cout << l << endl;
      cout << 1 << endl;
      cout << l;
    }
  }
  return 0;
}