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.util.*;
import java.io.*;

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);
		Task solver = new Task();

		int i = 0;
		int t = in.nextInt();
		for (; i < t; i++)
			solver.solve(i, in, out);

		out.close();
	}

	static class Task {
		public void solve(int testNumber, InputReader in, PrintWriter out) {
			long a = in.nextLong();
			long b = in.nextLong();
			long m = in.nextLong();

			if (a == b) {
				out.print(1 + " " + a);
				out.println();
				return;
			}
			int k = 1;
			long res = a + m;
			long mult = 1;
			for (; b > res; k++) {
				res *= 2;
				mult *= 2;
			}
			//out.println("mult: " + mult + "k: " + k);
			mult /= 2;

			if (b < (a + 1) * (res / (a + m))) {
				out.print(-1);
				out.println();
				return;
			}

			long w = b - (a + 1) * (res / (a + m));
			// out.println(w);

			long[] ar = new long[k + 1];
			for (; k > 0; k--) {
				if (k == 1) {
					ar[k] = w;

				} else if (k == 2 && m != 1) {
					if (w == 2*(m - 1)) {
						ar[k] = m - 1;
					} else {
						ar[k] = w % (m - 1);
					}
					w -= ar[k];

				} else {
					ar[k] = w / mult < m ? w / mult : m - 1;
					w -= ar[k] * mult;
					mult /= 2;
					// out.println(mult);
				}
			}
			//out.println(Arrays.toString(ar));
			long[] ans = new long[ar.length];
			ans[0] = a;
			ans[1] = a + ar[ar.length - 1] + 1;
			for (int i = 2; i < ans.length; i++) {
				ans[i] = 2 * ans[i - 1] + ar[ar.length - i] - ar[ar.length + 1 - i];
			}

			out.print(ans.length + " ");
			for (int i = 0; i < ans.length; i++) {
				out.print(ans[i] + " ");
			}

			out.println();

		}
	}

	// template code

	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());
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

	}

	static long modexp(long a, long b, long p) {
		// returns a to the power b mod p by modular exponentiation

		long res = 1;
		long mult = a % p;
		while (b > 0) {
			if (b % 2 == 1) {
				res = (res * mult) % p;
			}
			b /= 2;
			mult = (mult * mult) % p;
		}

		return res;
	}

	static double log(double arg, double base) {
		// returns log of a base b, contains floating point errors, dont use for exact
		// calculations.

		if (base < 0 || base == 1) {
			throw new ArithmeticException("base cant be 1 or negative");
		}
		if (arg < 0) {
			throw new ArithmeticException("log of negative number undefined");
		}
		return Math.log10(arg) / Math.log10(base);
	}

}