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.*;
import java.lang.reflect.Array;
import java.util.*;

public class Main {
    static int inf = (int) 1e9 + 7;
    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(System.out);
        int q = nextInt();
        for(int test = 0;test < q;test++) {
            long a = nextLong();
            long b = nextLong();
            long m = nextLong();
            int n = 0;
            if (a == b) {
                pw.println(1 + " " + a);
            }else {
                while (true) {
                    if ((1l << n) * (a + 1) <= b && b <= (1l << n) * (a + m)) break;
                    if (b < (1l << n) * (a + 1)) break;
                    n++;
                }
                if (b < (1l << n) * (a + 1)) pw.println(-1);
                else {
                    long r[] = new long[n + 1];
                    for (int i = 0; i <= n; i++) r[i] = 1;
                    b -= (1l << n) * (a + 1);
                    for (int i = 0; i <= n; i++) {
                        long cnt = b / (1l << (Math.max(n - i - 1, 0)));
                        if (cnt >= m) cnt-= cnt - m + 1;
                        r[i] += cnt;
                        b -= (1l << (Math.max(n - i - 1, 0))) * cnt;
                    }
                    long ans[] = new long[n + 2];
                    ans[0] = a;
                    pw.print(n + 2 + " " + a + " ");
                    for (int i = 1; i < n + 2; i++) {
                        for (int j = 0; j < i; j++) ans[i] += ans[j];
                        ans[i] += r[i - 1];
                        pw.print(ans[i] + " ");
                    }
                    pw.println();
                }
            }
        }
        pw.close();
    }

    static BufferedReader br;
    static StringTokenizer st = new StringTokenizer("");
    static PrintWriter pw;

    static String next() throws IOException {
        while (!st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

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

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