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 D561 {
    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
        int q = sc.nextInt();
        for (int i = 0; i < q; i++) {
            long a = sc.nextLong(); long b = sc.nextLong();
            long m = sc.nextLong();
            if (a == b) {
                out.println(1 + " " + a);
                continue;
            }
            int find = -1;
            for (int pow = 0; pow <= 50; pow++) {
                if (a * (1L << pow) > 1e14) break;
                long mul = (1L << pow);
                if (b >= (a + 1) * mul && b <= (a + m) * mul) {
                    find = pow; break;
                }
            }
            if (find == -1) {
                out.println(-1);
            } else {
                long cur = b; long pow = (1L << find);
                long [] ret = new long[find + 2];
                int idx = ret.length - 1;
                while (pow > 1) {
                    ret[idx] = cur;
                    cur = (cur) / 2;
                    pow /= 2;
                    idx--;
                }
                ret[1] = cur;
                ret[0] = a;
                long sum = a;
                for (int j = 1; j < ret.length - 1; j++) {
                    long prev = sum;
                    sum += ret[j];
                    if (sum + m <= ret[j + 1] && m != 1 && prev + m >= ret[j] + 1) {
                        ret[j]++; sum++;
                    }
                }
                out.print(ret.length + " ");
                for (Long j: ret) out.print(j + " ");
                out.println();
            }
        }

        out.close();
    }




    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }


    }

}