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;
long long l, r;
int k;
void solve1() {
  cout << l << "\n";
  cout << "1\n" << l;
  exit(0);
}
void solve2() {
  if (l % 2LL == 1 && l + 1 < r) l++;
  if (l % 2LL == 0) {
    cout << "1\n2\n";
    cout << l << " " << l + 1;
    exit(0);
  }
  if (l <= (l ^ r))
    solve1();
  else {
    cout << (l ^ r) << "\n2\n";
    cout << l << " " << r;
  }
  exit(0);
}
void solve3() {
  for (long long x = 1; x <= r; x *= 2LL) {
    long long nxt = x * 2LL;
    if (nxt - 1 >= l && nxt + x <= r) {
      cout << "0\n3\n";
      cout << nxt - 1 << " " << nxt + x - 1 << " " << nxt + x;
      exit(0);
    }
  }
  solve2();
}
void solve4() {
  for (long long x = l; x + 3 <= r; x++) {
    if ((x ^ (x + 1) ^ (x + 2) ^ (x + 3)) == 0) {
      cout << "0\n4\n";
      cout << x << " " << x + 1 << " " << x + 2 << " " << x + 3;
      exit(0);
    }
  }
  solve3();
}
int main() {
  ios_base::sync_with_stdio(0);
  cin >> l >> r >> k;
  if (k == 1) solve1();
  if (k == 2) solve2();
  if (k == 3) solve3();
  solve4();
}