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, k, x, y;
int main() {
  scanf("%lld%lld%lld", &l, &r, &k), x = 1;
  if (k == 1 || l == r || (r - l == 1 && l % 2 && (l ^ r) >= l))
    return printf("%lld\n1\n%lld\n", l, l), 0;
  for (int i = 0;; i++) {
    if (x > l) {
      y = i;
      break;
    }
    x *= 2;
  }
  if (x + x / 2 <= r && k >= 3)
    return printf("0\n3\n%lld %lld %lld\n", x - 1, x + x / 2, x + x / 2 - 1), 0;
  if (r - l == 1)
    return printf("%lld\n2\n%lld %lld\n", l ^ (l + 1), l, l + 1), 0;
  if (l % 2) l++;
  if (l + 3 <= r && k >= 4)
    return printf("0\n4\n%lld %lld %lld %lld\n", l, l + 1, l + 2, l + 3), 0;
  else
    return printf("1\n2\n%lld %lld\n", l, l + 1), 0;
}