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;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int T;
  cin >> T;
  while (T--) {
    long long a, b, m;
    cin >> a >> b >> m;
    if (a == b) {
      cout << "1 " << a << endl;
      continue;
    }
    bool ok = 0;
    for (int i = 0; i < 50; i++) {
      if ((1LL << i) > 1e18 / (a + m)) break;
      if ((1LL << i) * (a + 1) <= b && b <= (1LL << i) * (a + m)) ok = 1;
    }
    if (ok == 0) {
      cout << -1 << endl;
      continue;
    }
    vector<long long> res;
    res.push_back(a);
    long long tot = a;
    while (1) {
      if (res.back() >= b) break;
      long long cur = tot + 1;
      res.push_back(cur);
      tot += cur;
    }
    if (res.back() > b) res.pop_back();
    long long rem = b - res.back();
    int n = res.size();
    for (int i = 0; i < 50; i++) {
      if ((rem & (1LL << i)) == 0) continue;
      long long cur = (1LL << i);
      for (int j = n - 1; j >= 1; j--) {
        if (cur == 0) {
          res[j]++;
          break;
        }
        res[j] += cur;
        cur /= 2;
      }
    }
    assert(res.back() == b);
    cout << res.size() << " ";
    for (auto &i : res) cout << i << " ";
    cout << endl;
  }
}