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{


	public static void main(String args[]){

		Scanner in=new Scanner(new BufferedReader(new InputStreamReader(System.in)));

		int q=in.nextInt();

		while(q--!=0){

			long a=in.nextLong(),
				 b=in.nextLong(),
				 m=in.nextLong();

			if(b<a){
				System.out.println(-1);
				continue;
			}
			else if(a==b){
				System.out.println("1 "+a);
				continue;
			}

			ArrayList<Long> item=new ArrayList<>();
			item.add(a);

			long power=0;

			while(true){
				long curr=(1L<<power)*a;
				item.add(curr);
				//System.out.println(power+" "+curr);

				if(curr+(1L<<power)*m>=b)
					break;

				power+=1L;
			}
			int n=item.size();
			long diff=(b-item.get(n-1));

			//System.out.println(item);
			if( diff/(1L<<power)<1L ){
				System.out.println(-1);
				continue;
			}

			ArrayList<Long> freq=new ArrayList<>();
			ArrayList<Long> mul=new ArrayList<>();

			for(long i=power; i>=1L; i--){
				freq.add(1L<<(i-1));
				mul.add(diff/(1L<<power));
			}
			freq.add(1L);
			mul.add(diff/(1L<<power));

			long rem=diff%(1L<<power);

			for(int i=0; i<freq.size(); i++)
				if(freq.get(i)<=rem){
					mul.set(i, mul.get(i)+1);
					rem-=freq.get(i);
				}

			for(int i=1; i<freq.size(); i++)
				for(int j=0; j<i; j++)
					mul.set(i, mul.get(j)+mul.get(i));

			for(int i=1; i<item.size(); i++)
				item.set(i, item.get(i)+mul.get(i-1));


			System.out.print(item.size()+" ");
			for(long value:item)
				System.out.print(value+" ");
			System.out.println();

		}
	}
}