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.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author prakharjain
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        DCuteSequences solver = new DCuteSequences();
        solver.solve(1, in, out);
        out.close();
    }

    static class DCuteSequences {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int q = in.nextInt();

            o:
            while (q-- > 0) {
                long a = in.nextLong();
                long b = in.nextLong();

                long m = in.nextLong();

                i:
                for (int i = 1; i <= 50; i++) {
                    long[] seq = new long[i];

                    seq[0] = a;
                    long sum = a;
                    for (int j = 1; j < i; j++) {
                        seq[j] = sum + 1;
                        sum += seq[j];
                        if (seq[j] > b) {
                            continue i;
                        }
                    }

                    long min = seq[i - 1];

//                long lpt = 0;
//
//                while ((1L << lpt) <= m - 1) {
//                    lpt++;
//                }
//
//                lpt--;
//
//                long ext = 1L << lpt;

                    //long max = min + (m - 1) * (i - 1);

                    long rem = b - min;

                    if (rem >= 0) {
                        long[] ex = new long[i];

                        for (int j = 1; j < i; j++) {
                            int diff = Math.max(0, i - 1 - j - 1);
                            long pow = 1L << diff;

                            if (rem >= pow) {
                                long mul = rem / pow;

                                if (mul > m - 1) {
                                    ex[j] = m - 1;
                                    rem -= (m - 1) * pow;
                                } else {
                                    ex[j] = mul;
                                    rem -= mul * pow;
                                }
                            }
                        }

//                    for (int j = 1; j < i; j++) {
//                        int diff = Math.max(0, i - 1 - j - 1);
//                        long pow = 1L << diff;
//
//                        if (rem >= pow && (m - 1) > 0) {
////                            long mul = rem / pow;
////
////                            long lpt2 = 0;
////
////                            while ((1L << lpt2) <= mul) {
////                                lpt2++;
////                            }
////
////                            lpt2--;
////
////                            long nmul = 1L << lpt2;
//
////                            if (nmul >= ext) {
////                                ex[j] = ext;
////                                rem -= ext * pow;
////                            } else {
////                                ex[j] = nmul;
////                                rem -= nmul * pow;
////                            }
//
//                            rem -= pow;
//                            ex[j]++;
//                        }
//                    }

                        if (rem != 0) {
                            continue;
                        }

                        out.print(i + " ");

                        seq[0] = a;
                        sum = a;
                        for (int j = 1; j < i; j++) {
                            seq[j] = sum + ex[j] + 1;
                            sum += seq[j];
                        }

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

                        out.println();
                        continue o;
                    }
                }

                out.println(-1);
            }
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void println() {
            writer.println();
        }

        public void close() {
            writer.close();
        }

        public void println(int i) {
            writer.println(i);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}