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 ans[60];
int main() {
  long long t, a, n, m, b, v, xmin, xmax, act, sum, i, vmi;
  cin >> t;
  while (t--) {
    cin >> a >> b >> m;
    if (a == b) {
      cout << "1 " << a << '\n';
      continue;
    }
    for (n = 2; n <= 50; n++) {
      v = ((1ll) << (n - 2));
      xmin = v * a + v;
      xmax = v * a + v * m;
      if (xmin > b) {
        n = 51;
        break;
      }
      if (b <= xmax) {
        act = xmax;
        ans[1] = a;
        sum = ans[1];
        for (i = 2; i <= n; i++) {
          v = ((1ll) << (max(n - i - 1, 0ll)));
          vmi = m - (act - b) / v;
          vmi = max(vmi, 1ll);
          ans[i] = sum + vmi;
          sum = sum + ans[i];
          act -= (m - vmi) * v;
        }
        if (i <= n || ans[n] != b) continue;
        cout << n << ' ';
        for (i = 1; i <= n; i++) cout << ans[i] << ' ';
        cout << '\n';
        break;
      }
    }
    if (n == 51) {
      cout << -1 << '\n';
    }
  }
  return 0;
}