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, len;
  cin >> l >> r >> k;
  len = r - l + 1;
  if (k == 1) {
    cout << l << endl << 1 << endl << l << endl;
    return 0;
  } else if (k == 2) {
    if (l == 1)
      cout << 1 << endl << 1 << endl << 1 << endl;
    else if (len == 2 && (l & 1)) {
      long long ans = l ^ (l + 1);
      if (l < ans)
        cout << l << endl << 1 << endl << l << endl;
      else
        cout << ans << endl << 2 << endl << l << " " << l + 1 << endl;
      return 0;
    } else if (l & 1) {
      cout << 1 << endl << 2 << endl << l + 1 << " " << l + 2 << endl;
      return 0;
    } else {
      cout << 1 << endl << 2 << endl << l << " " << l + 1 << endl;
      return 0;
    }
  } else if (k == 3) {
    bool ff = false;
    long long i, x, y, a, b, c;
    for (i = 62; i >= 0; i--) {
      x = 1ll << i, y = 1ll << i - 1, a = x | y, b = x | y - 1, c = x - 1;
      if (l <= a && a <= r && l <= b && b <= r && l <= c && c <= r &&
          (a ^ b ^ c) == 0) {
        ff = 1;
        cout << 0 << endl << 3 << endl << a << " " << b << " " << c << endl;
        return 0;
      }
    }
    if (!ff) {
      if (l & 1)
        cout << 1 << endl << 2 << endl << l + 1 << " " << l + 2 << endl;
      else
        cout << 1 << endl << 2 << endl << l << " " << l + 1 << endl;
      return 0;
    }
  } else if (len >= 4 && k >= 4) {
    if (l % 2 == 0)
      cout << 0 << endl
           << 4 << endl
           << l << " " << l + 1 << " " << l + 2 << " " << l + 3 << endl;
    else if (len > 4)
      cout << 0 << endl
           << 4 << endl
           << l + 1 << " " << l + 2 << " " << l + 3 << " " << l + 4 << endl;
    else if (len == 4 && k == 4 && l % 2 == 1)
      goto lb;
    return 0;
  } else if (len == 4 && (l & 1LL)) {
  lb:
    long long a = l, b = l + 1, c = l + 2, d = r;
    if ((a ^ b ^ c) == 0) {
      cout << 0 << endl << 3 << endl << a << " " << b << " " << c << endl;
      return 0;
    } else if ((a ^ b ^ d) == 0) {
      cout << 0 << endl << 3 << endl << a << " " << b << " " << d << endl;
      return 0;
    } else if ((a ^ d ^ c) == 0) {
      cout << 0 << endl << 3 << endl << a << " " << c << " " << d << endl;
      return 0;
    } else if ((d ^ b ^ c) == 0) {
      cout << 0 << endl << 3 << endl << b << " " << c << " " << d << endl;
      return 0;
    } else {
      cout << 1 << endl << 2 << endl << b << " " << c << endl;
      return 0;
    }
  }
  return 0;
}