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 Solution{
    static Scanner sc;
    static PrintWriter pw;
    
    public static void main(String args[]){
        sc = new Scanner(System.in);
        pw = new PrintWriter(System.out);
        
        int t = sc.nextInt();
        while(t-->0)
            solve();
            
        pw.flush();
        pw.close();
    }
    public static void solve(){
        long a = sc.nextLong(), b = sc.nextLong(), m = sc.nextLong();
        
        if(a == b){
            pw.println(+1+" "+Long.toString(a));
            return;
        }
        
        for(int i=1; i<=60; i++){
            long low = (long)Math.pow(2, i-1)*(a+1), high = (long)Math.pow(2, i-1)*(a+m);
            
            if(low <= b && b<= high){
                
                if(i == 1){
                    pw.println(+2+" "+a+" "+b);
                    return;
                }
                
                long k = b - (long)Math.pow(2, i-1)*(a+1);
                //System.out.println(+k+" "+i);
                
                long arr[] = new long[i+1], sum[] = new long[i+1], step[] = new long[i], fact[] = new long[i];
                arr[0] = a;
                
                fact[i-1] = 1;
                step[i-1] = 1;
                long q = 1;
                for(int j=i-2; j>=0; j--, q=q*2){
                    step[j] = 1;
                    fact[j] = q;
                }
                    
                for(int j=0; j<i; j++){
                    long p = Math.min(k/fact[j], m-1);
                    step[j] += p;
                    k -= fact[j]*p;
                }
                
                sum[0] = arr[0];
                for(int j=1; j<=i; j++){
                    //System.out.println(+step[j-1]);
                    arr[j] = sum[j-1] + step[j-1];
                    sum[j] = sum[j-1] + arr[j];
                }
                
                pw.print(+(i+1)+" ");
                for(long u: arr)
                    pw.print(+u+" ");
                pw.println();
                return;
            }
            else if(low > b)
                break;
        }
        pw.println(-1);
    }
}