Problem: Given a positive integer m, we say that a sequence x_1, x_2, ..., x_n of positive integers is m-cute if for every index i such that 2 ≤ i ≤ n it holds that x_i = x_{i - 1} + x_{i - 2} + ... + x_1 + r_i for some positive integer r_i satisfying 1 ≤ r_i ≤ m.

You will be given q queries consisting of three positive integers a, b and m. For each query you must determine whether or not there exists an m-cute sequence whose first term is a and whose last term is b. If such a sequence exists, you must additionally find an example of it.

Input

The first line contains an integer number q (1 ≤ q ≤ 10^3) — the number of queries.

Each of the following q lines contains three integers a, b, and m (1 ≤ a, b, m ≤ 10^{14}, a ≤ b), describing a single query.

Output

For each query, if no m-cute sequence whose first term is a and whose last term is b exists, print -1.

Otherwise print an integer k (1 ≤ k ≤ 50), followed by k integers x_1, x_2, ..., x_k (1 ≤ x_i ≤ 10^{14}). These integers must satisfy x_1 = a, x_k = b, and that the sequence x_1, x_2, ..., x_k is m-cute.

It can be shown that under the problem constraints, for each query either no m-cute sequence exists, or there exists one with at most 50 terms.

If there are multiple possible sequences, you may print any of them.

Example

Input


2
5 26 2
3 9 1


Output


4 5 6 13 26
-1

Note

Consider the sample. In the first query, the sequence 5, 6, 13, 26 is valid since 6 = 5 + \bf{\color{blue} 1}, 13 = 6 + 5 + {\bf\color{blue} 2} and 26 = 13 + 6 + 5 + {\bf\color{blue} 2} have the bold values all between 1 and 2, so the sequence is 2-cute. Other valid sequences, such as 5, 7, 13, 26 are also accepted.

In the second query, the only possible 1-cute sequence starting at 3 is 3, 4, 8, 16, ..., which does not contain 9.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
long long s[100];
int main() {
  int q;
  cin >> q;
  while (q--) {
    long long a, b, m;
    cin >> a >> b >> m;
    if (a == b) {
      cout << 1 << ' ' << a << endl;
      continue;
    }
    long long l = a, r = a;
    int k = 1;
    while (r + m < b) {
      l = l * 2 + 1;
      r = r * 2 + m;
      k++;
    }
    if (b < l + 1)
      puts("-1");
    else {
      s[1] = a;
      for (int i = 2; i <= k; i++) {
        for (long long L = 1, R = m, mid; L <= R;) {
          mid = (L + R) / 2;
          l = r = s[i - 1] * 2 + mid;
          for (int j = i + 1; j <= k; j++) {
            l = l * 2 + 1, r = r * 2 + m;
          }
          if (b < l + 1)
            R = mid - 1;
          else if (r + m < b)
            L = mid + 1;
          else {
            s[i] = s[i - 1] * 2 + mid;
            break;
          }
        }
      }
      cout << k + 1 << ' ';
      for (int i = 1; i <= k; i++) cout << s[i] - s[i - 1] << ' ';
      cout << b << endl;
    }
  }
  return 0;
}