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;
const int M = 998244353;
int n;
int bin_search_upper(int tar, vector<int>& a) {
  int lo = 0, hi = n - 1;
  int mid = (lo + hi + 1) >> 1;
  while (lo < hi) {
    mid = (lo + hi + 1) >> 1;
    if (a[mid] == tar)
      return mid;
    else if (a[mid] < tar)
      lo = mid;
    else
      hi = mid - 1;
  }
  return lo;
}
int bin_search_lower(int tar, vector<int>& a) {
  int lo = 0, hi = n - 1;
  int mid = (lo + hi) >> 1;
  while (lo < hi) {
    mid = (lo + hi) >> 1;
    if (a[mid] == tar)
      return mid;
    else if (a[mid] < tar)
      lo = mid + 1;
    else
      hi = mid;
  }
  return lo;
}
int main() {
  int q;
  cin >> q;
  while (q--) {
    long long int a, b_, m;
    cin >> a >> b_ >> m;
    if (a == b_) {
      cout << "1 " << a << "\n";
      continue;
    }
    bool flag = false;
    vector<long long int> cnt;
    for (int k = 2; k <= 50; ++k) {
      cnt.clear();
      long long int b = b_;
      long long int p = 1LL << k - 2;
      if (a * p >= b) break;
      b -= a * p;
      cnt.push_back(a);
      if (b < p) continue;
      b -= p;
      p >>= 1;
      while (p >= 1) {
        long long int j = b / p;
        if (j > m - 1) j = m - 1;
        b -= p * j;
        cnt.push_back(j + 1);
        p >>= 1;
      }
      if (b > m - 1) continue;
      cnt.push_back(b + 1);
      flag = true;
      break;
    }
    if (flag) {
      long long int sum = a;
      for (int i = 1; i < cnt.size(); ++i) {
        cnt[i] += sum;
        sum += cnt[i];
      }
      cout << cnt.size();
      for (int i = 0; i < cnt.size(); ++i) cout << " " << cnt[i];
      cout << "\n";
    } else
      cout << "-1\n";
  }
}