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;
vector<vector<long long>> ans;
bool cmp(vector<long long> a, vector<long long> b) {
  long long sum1 = 0, sum2 = 0;
  for (auto i : a) sum1 ^= i;
  for (auto i : b) sum2 ^= i;
  return sum1 < sum2;
}
int siz(long long p) {
  int pp = 0;
  while (p != 1ll) {
    p >>= 1ll;
    ++pp;
  }
  return pp;
}
int main() {
  long long l, r, k;
  cin >> l >> r >> k;
  vector<long long> tmp;
  if (k >= 1) {
    tmp.push_back(l);
    ans.emplace_back(tmp);
    tmp.clear();
  }
  if (k >= 2) {
    tmp.push_back(l);
    tmp.push_back(l + 1);
    ans.emplace_back(tmp);
    tmp.clear();
    if (l + 2 <= r) {
      tmp.push_back(l + 1);
      tmp.push_back(l + 2);
      ans.emplace_back(tmp);
      tmp.clear();
    }
  }
  if (k >= 3) {
    long long tmpp = siz(l);
    if ((1ll << (tmpp)) + (1ll << (tmpp + 1)) <= r) {
      tmp.push_back(l);
      tmp.push_back((1ll << (tmpp)) + (1ll << (tmpp + 1)));
      tmp.push_back(l + (1ll << (tmpp + 1)) - (1ll << (tmpp)));
      ans.emplace_back(tmp);
      tmp.clear();
    }
  }
  if (k >= 4) {
    tmp.push_back(l + 1);
    tmp.push_back(l + 2);
    tmp.push_back(l + 3);
    tmp.push_back(l);
    ans.emplace_back(tmp);
    if (l + 4 <= r) {
      tmp.pop_back();
      tmp.push_back(l + 4);
      ans.emplace_back(tmp);
    }
  }
  sort(ans.begin(), ans.end(), cmp);
  long long lans = 0;
  for (auto i : ans[0]) lans ^= i;
  cout << lans << '\n';
  cout << ans[0].size() << '\n';
  for (auto i : ans[0]) cout << i << ' ';
}