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 MaxBit(long long x) {
  int res = 0;
  while (x != 0) {
    x /= 2;
    res++;
  }
  return res;
}
int main() {
  long long l, r, k;
  cin >> l >> r >> k;
  long long len = r - l + 1;
  long long res = l;
  vector<long long> res_record = {l};
  if (len <= 4) {
    for (int i = 1; i < (1 << len); i++) {
      long long xor_res = 0;
      vector<long long> xor_record;
      for (int j = 0; j < len; j++) {
        if (i & (1 << j)) {
          xor_res ^= l + j;
          xor_record.push_back(l + j);
        }
      }
      if (res > xor_res && int(xor_record.size()) <= k) {
        res = xor_res;
        res_record = xor_record;
      }
    }
  } else if (k == 2) {
    res = 1;
    if (l & 1) {
      res_record = {l + 1, l + 2};
    } else {
      res_record = {l, l + 1};
    }
  } else if (k == 3) {
    res = 1;
    if (l & 1) {
      res_record = {l + 1, l + 2};
    } else {
      res_record = {l, l + 1};
    }
    int max_bit = MaxBit(l) - 1;
    if ((3LL << max_bit) <= r) {
      res = 0;
      res_record = {l, 3LL << max_bit, (3LL << max_bit) ^ l};
    }
  } else if (k >= 4) {
    res = 0;
    if (l & 1) {
      res_record = {l + 1, l + 2, l + 3, l + 4};
    } else {
      res_record = {l, l + 1, l + 2, l + 3};
    }
  }
  cout << res << endl;
  cout << res_record.size() << endl;
  for (const auto& i : res_record) {
    cout << i << " ";
  }
  cout << endl;
}