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 JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DMiliePosledovatelnosti solver = new DMiliePosledovatelnosti();
        solver.solve(1, in, out);
        out.close();
    }

    static class DMiliePosledovatelnosti {

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int q = in.nextInt();
            for (int t = 0; t < q; t++) {
                long st = in.nextLong();
                long end = in.nextLong();
                long m = in.nextLong();
                long[] a = new long[51];
                if (end == st) {
                    out.print(1);
                    out.print(" ");
                    out.println(st);
                    continue;
                }
                a[0] = st;
                a[1] = st + 1;
                int n = 2;
                while (a[n - 1] * 2 <= end) {
                    a[n] = a[n - 1] * 2;
                    n++;
                }
                long diff = end - a[n - 1];
                long[] incs = new long[51];
                for (int i = 1; i < n; i++) {
                    long pow = Math.max(0, (n - i) - 2);
                    long d = (long) Math.pow(2, pow);
                    long inc = Math.min(m - 1, diff / d);
                    incs[i] = inc;
                    diff -= d * inc;
                }
                if (diff != 0) {
                    out.println(-1);
                    continue;
                }
                a[1] += incs[1];
                long sum = a[0] + a[1];
                for (int i = 2; i < n; i++) {
                    a[i] = sum + 1 + incs[i];
                    sum += a[i];
                }
                out.print(n);
                out.print(' ');
                for (int i = 0; i < n; i++) {
                    out.print(a[i]);
                    out.print(' ');
                }
                out.println();
            }
        }
    }

    static class InputReader {

        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }
    }
}