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

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author cplayer
 */
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();
        int testCount = Integer.parseInt(in.next());
        for (int i = 1; i <= testCount; i++)
            solver.solve(i, in, out);
        out.close();
    }

    static class DCuteSequences {
        public void solve (int testNumber, InputReader in, OutputWriter out) {
            long a = in.readLong(), b = in.readLong(), m = in.readLong();
            if (a == b) {
                out.println(1, ' ', a);
                return;
            } else {
                long pow2 = 1;
                // 遍历所有可能的n
                for (int i = 2; i <= 50; ++i) {
                    // 若最小的还比b大没有比较的必要
                    if (pow2 * (a + 1) > b) {
                        break;
                    }
                    // 可以求出对应的a + k以及r
                    long div = b / pow2;
                    long mod = b % pow2;
                    if (div >= a) {
                        // 根据div和mod构造对应的r，必须要求div >= a
                        long[] r = new long[i];
                        Arrays.fill(r, div - a);
                        int[] bits = IntegerUtils.getBinaryNumberBits(mod, i - 2);
                        for (int j = 1; j < i; ++j) {
                            if (i - 2 - j == -1) {
                                r[j] += 0;
                            } else {
                                r[j] += bits[j - 1];
                            }
                        }
                        // 必须全在[1, m]之间
                        boolean judge = true;
                        for (int j = 0; j < i; ++j) {
                            if (r[j] < 1 || r[j] > m) {
                                judge = false;
                                break;
                            }
                        }
                        if (judge) {
                            // 成功，输出并返回
                            long[] res = new long[i];
                            res[0] = a;
                            for (int j = 1; j < i; ++j) {
                                for (int k = 0; k < j; ++k) {
                                    res[j] += res[k];
                                }
                                res[j] += r[j];
                            }
                            out.print(i);
                            out.print(' ');
                            out.println(res);
                            return;
                        }
                    }
                    pow2 *= 2;
                }
            }
            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 print (long[] array) {
            for (int i = 0; i < array.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(array[i]);
            }
        }

        public void println (long[] array) {
            print(array);
            writer.println();
        }

        public void println (Object... objects) {
            print(objects);
            writer.println();
        }

        public void print (char i) {
            writer.print(i);
        }

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

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

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

    }

    static class IntegerUtils {
        public static int[] getBinaryNumberBits (long number, int size) {
            int[] res = new int[size];
            int pt = res.length - 1;
            while (pt >= 0) {
                res[pt] = (int) (number & 1);
                number = number >> 1;
                --pt;
            }
            return res;
        }

    }

    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 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 long readLong () {
            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 String readString () {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                if (Character.isValidCodePoint(c)) {
                    res.appendCodePoint(c);
                }
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

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

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

        public String next () {
            return readString();
        }

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

        }

    }
}