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;
unsigned long long a, b, m;
void find() {
  vector<unsigned long long> min;
  min.push_back(a);
  min.push_back(a + 1);
  while (min.back() < b) {
    min.push_back(2 * min.back());
  }
  vector<unsigned long long> max;
  max.push_back(a);
  max.push_back(a + m);
  while (max.back() < b) {
    max.push_back(2 * max.back());
  }
  unsigned int idx = 100;
  for (unsigned int i = 0; i < max.size(); i++) {
    if (min[i] <= b && max[i] >= b) {
      idx = i;
      break;
    }
  }
  if (idx >= 50) {
    cout << -1 << endl;
    return;
  }
  cout << idx + 1 << " ";
  vector<unsigned long long> seq;
  seq.resize(idx + 1);
  seq[idx] = b;
  bool flo = true;
  for (int i = 1; i < idx; i++) {
    if (seq[idx - i + 1] % 2 == 0) {
      seq[idx - i] = seq[idx - i + 1] / 2;
      continue;
    }
    if (flo) {
      seq[idx - i] = seq[idx - i + 1] / 2;
      flo = false;
    } else {
      seq[idx - i] = (seq[idx - i + 1] + 1) / 2;
      flo = true;
    }
  }
  seq[0] = a;
  for (unsigned int i = 0; i < seq.size(); i++) {
    cout << seq[i];
    if (i + 1 != seq.size()) {
      cout << " ";
    } else {
      cout << endl;
    }
  }
}
int main() {
  int q;
  cin >> q;
  for (int i = 0; i < q; i++) {
    cin >> a >> b >> m;
    find();
  }
  cin.ignore(2);
  return 0;
}