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:
/**
 * @author derrick20
 */
import java.io.*;
import java.util.*;

public class CuteSequences implements Runnable {
    public static void main(String[] args) throws Exception {
        new Thread(null, new CuteSequences(), ": )", 1 << 28).start();
    }

    public void run() {
        FastScanner sc = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);

        int Q = sc.nextInt();
        while (Q-->0) {
            long a = sc.nextLong();
            long b = sc.nextLong();
            long m = sc.nextLong();
            if (a == b) {
                // crap
                out.println(1 + " " + a);
            } else {
                // k is len - 1
                ArrayDeque<Long> ans = new ArrayDeque<>();
                long k = 0;
                while (k + 1 <= 50 && (1L << k) * (a + m) < b) {
                    k++;
                }
                long curr = (1L << k) * (a + 1);
                if (curr > b) {
                    // it may have skipped past
                    out.println(-1);
                } else {
                    // at this point, it must cover b (2^50 is 10^15, so we're good)
                    ArrayList<Long> steps = new ArrayList<>();
//                    System.out.println(curr);
                    for (int pos = 0; pos <= k; pos++) {
                        // pattern:
                        // pos: 0 1 2 3
                        // contrib: 4 2 1 1 (since the last one doesn't get time to multiply)
                        long contrib = 1L << (Math.max(0, k - pos - 1));
                        // we want to add as much as we can at this first
                        // branch point without exceeding the gap, greedy!
                        // (Works since we are starting from the base point
                        // of adding 1 to each!)
                        long gain = (b - curr) / contrib;
                        gain = Math.min(gain, m - 1);
                        steps.add(gain);
//                        System.out.println(steps);
                        ASSERT(gain <= m - 1);
                        curr += gain * contrib;
//                        System.out.println(curr);
                    }
                    ASSERT(b == curr);
                    long val = a;
                    long total = val;
                    ans.add(total);
                    val += steps.get(0) + 1;
                    total += val;
                    ans.add(val);
//                    System.out.println(steps);
                    for (int i = 1; i < steps.size(); i++) {
                        val = total + steps.get(i) + 1;
                        total += val;
                        ans.add(val);
                    }
                    // last bit is just a, every time
                    StringBuilder sb = new StringBuilder();
                    sb.append(ans.size()).append(" ");
                    for (long x : ans) {
                        sb.append(x).append(" ");
                    }
                    out.println(sb);
                }
            }
        }

        out.close();
    }

    static class FastScanner {
        private int BS = 1 << 16;
        private char NC = (char) 0;
        private byte[] buf = new byte[BS];
        private int bId = 0, size = 0;
        private char c = NC;
        private double cnt = 1;
        private BufferedInputStream in;

        public FastScanner() {
            in = new BufferedInputStream(System.in, BS);
        }

        public FastScanner(String s) {
            try {
                in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
            } catch (Exception e) {
                in = new BufferedInputStream(System.in, BS);
            }
        }

        private char getChar() {
            while (bId == size) {
                try {
                    size = in.read(buf);
                } catch (Exception e) {
                    return NC;
                }
                if (size == -1) return NC;
                bId = 0;
            }
            return (char) buf[bId++];
        }

        public int nextInt() {
            return (int) nextLong();
        }

        public int[] nextInts(int N) {
            int[] res = new int[N];
            for (int i = 0; i < N; i++) {
                res[i] = (int) nextLong();
            }
            return res;
        }

        public long[] nextLongs(int N) {
            long[] res = new long[N];
            for (int i = 0; i < N; i++) {
                res[i] = nextLong();
            }
            return res;
        }

        public long nextLong() {
            cnt = 1;
            boolean neg = false;
            if (c == NC) c = getChar();
            for (; (c < '0' || c > '9'); c = getChar()) {
                if (c == '-') neg = true;
            }
            long res = 0;
            for (; c >= '0' && c <= '9'; c = getChar()) {
                res = (res << 3) + (res << 1) + c - '0';
                cnt *= 10;
            }
            return neg ? -res : res;
        }

        public double nextDouble() {
            double cur = nextLong();
            return c != '.' ? cur : cur + nextLong() / cnt;
        }

        public double[] nextDoubles(int N) {
            double[] res = new double[N];
            for (int i = 0; i < N; i++) {
                res[i] = nextDouble();
            }
            return res;
        }

        public String next() {
            StringBuilder res = new StringBuilder();
            while (c <= 32) c = getChar();
            while (c > 32) {
                res.append(c);
                c = getChar();
            }
            return res.toString();
        }

        public String nextLine() {
            StringBuilder res = new StringBuilder();
            while (c <= 32) c = getChar();
            while (c != '\n') {
                res.append(c);
                c = getChar();
            }
            return res.toString();
        }

        public boolean hasNext() {
            if (c > 32) return true;
            while (true) {
                c = getChar();
                if (c == NC) return false;
                else if (c > 32) return true;
            }
        }
    }

    static void ASSERT(boolean assertion, String message) {
        if (!assertion) throw new AssertionError(message);
    }

    static void ASSERT(boolean assertion) {
        if (!assertion) throw new AssertionError();
    }
}