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 n;
int main() {
  long long l, r, k;
  scanf("%lld", &l);
  scanf("%lld", &r);
  scanf("%lld", &k);
  if (k == 1) {
    cout << l << endl;
    cout << 1 << endl;
    cout << l << endl;
    return 0;
  }
  long long b, e;
  b = ceil(l / 4.0);
  e = r / 4;
  if (e > b) {
    if (k >= 4) {
      long long start = 4 * b;
      cout << 0 << endl
           << 4 << endl
           << (start) << " " << (start + 1) << " " << (start + 2) << " "
           << (start + 3) << " ";
      return 0;
    } else if (k == 3) {
      long long x = 0, y = 0, z = 0;
      long long a = l;
      long long b = r;
      long long mn = 1;
      long long mx = 3;
      while (mx <= b) {
        if (mn >= a) {
          cout << 0 << endl;
          cout << 3 << endl;
          cout << mn << " " << mx - 1 << " " << mx << endl;
          return 0;
        }
        mn <<= 1;
        mn++;
        mx <<= 1;
      }
      b = ceil(l / 4.0);
      long long start = 4 * b;
      cout << 1 << endl << 2 << endl << (start) << " " << (start + 1) << " ";
    } else if (k == 2) {
      long long start = 4 * b;
      cout << 1 << endl << 2 << endl << (start) << " " << (start + 1);
    }
  } else {
    int q = r - l + 1;
    long long mini = (long long)1e18, bit = 1;
    for (int i = 1; i < (1 << q); i++) {
      if (__builtin_popcount(i) > k) continue;
      int temp = i;
      long long val = 0;
      for (int j = 0; j < 30; j++) {
        if (((i >> j) & 1)) {
          val = val ^ (l + j);
        }
      }
      if (mini > val) {
        mini = val;
        bit = i;
      }
    }
    cout << mini << endl;
    cout << __builtin_popcount(bit) << endl;
    for (int j = 0; j < 30; j++) {
      if (((bit >> j) & 1)) {
        cout << (l + j) << " ";
      }
    }
  }
}