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;
const int INF = 1e9;
const int mod = 1e9 + 7;
int T;
long long int L, R;
int k;
void work() {
  if (k == 3) {
    long long int x = -1, y, z;
    for (long long int i = 3; i <= R; i <<= 1) {
      if ((i ^ (i - 1)) >= L) {
        x = i;
        y = i - 1;
        z = i ^ (i - 1);
        break;
      }
    }
    if (x != -1) {
      cout << 0 << " " << 3 << endl;
      cout << x << " " << y << " " << z << endl;
    } else {
      if (L & 1) L++;
      cout << 1 << " " << 2 << endl;
      cout << L << " " << L + 1 << endl;
    }
  } else {
    if (R - L + 1 == 4) {
      if (L % 2 == 0) {
        cout << 0 << " " << 4 << endl;
        cout << L << " " << L + 1 << " " << L + 2 << " " << L + 3 << endl;
      } else {
        int flag = 0;
        long long int x, i, j;
        for (i = L; i <= R; i++) {
          for (j = i + 1; j <= R; j++) {
            x = i ^ j;
            if (L <= x && x <= R && x != i && x != j) {
              flag = 1;
              break;
            }
          }
          if (flag) break;
        }
        if (flag) {
          cout << 0 << " " << 3 << endl;
          cout << i << " " << j << " " << x << endl;
        } else {
          cout << 1 << " " << 2 << endl;
          cout << L + 1 << " " << L + 2 << endl;
        }
      }
    } else {
      if (L % 2 == 1) {
        cout << 0 << " " << 4 << endl;
        cout << L + 1 << " " << L + 2 << " " << L + 3 << " " << L + 4 << endl;
      } else {
        cout << 0 << " " << 4 << endl;
        cout << L << " " << L + 1 << " " << L + 2 << " " << L + 3 << endl;
      }
    }
  }
}
int main() {
  scanf("%lld%lld%d", &L, &R, &k);
  if (k == 1) {
    cout << L << " " << 1 << endl;
    cout << L << endl;
  } else if (k == 2) {
    if (R - L + 1 == 2) {
      long long int minl = L ^ R;
      if (minl < L && minl < R) {
        cout << minl << " " << 2 << endl;
        cout << L << " " << R << endl;
      } else {
        cout << L << " " << 1 << endl;
        cout << L << endl;
      }
    } else if (L % 2 == 0) {
      cout << 1 << " " << 2 << endl;
      cout << L << " " << L + 1 << endl;
    } else {
      cout << 1 << " " << 2 << endl;
      cout << L + 1 << " " << L + 2 << endl;
    }
  } else
    work();
  return 0;
}