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 Main {
	public static void main(String args[]) {new Main().run();}

	FastReader in = new FastReader();
	PrintWriter out = new PrintWriter(System.out);
	void run(){
		int q=in.nextInt();
		for(int i=0;i<q;i++) {
			work();
		}
		out.flush();
	}
	long mod=998244353;
	long gcd(long a,long b) {
		return b==0?a:gcd(b,a%b);
	}
	void work() {
		long a=in.nextLong();
		long b=in.nextLong();
		long m=in.nextLong();
		if(a==b) {
			out.println(1+" "+a);
			return;
		}
		for(long i=2;i<=50;i++) {
			if(a*(1L<<(i-2))-(1L<<(i-2))>b)break;
			if(work(a,b,m,i)) {
				out.println();
				return;
			}
		}
		out.println(-1);
	}
	
	boolean work(long a,long b,long m,long n) {
		long[] ret=new long[(int)n];
		ret[0]=a;
		//先每个填1
		//15 51 55 110 219 439 877 1754 3509 7017 14034 28068 56137 112273 224547 449093 
		long r=b-a*(1L<<(n-2))-(1L<<(n-2));
		if(r<0) return false;
		for(int i=1;i<n;i++)ret[i]=1;
		for(int i=1;i<n-1;i++) {
			long v=1L<<(n-i-2);
			long c=Math.min(r/v, m-1);
			ret[i]+=c;
			r-=c*v;
		}
		if(r>m-1)return false;
		ret[(int)n-1]+=r;
		long cur=0;
		for(int i=1;i<n;i++) {
			cur+=ret[i-1];
			ret[i]+=cur;
		}
		out.print(n+" ");
		for(int i=0;i<n;i++) {
			out.print(ret[i]+" ");
		}
		return true;
	}
}



class FastReader
{
	BufferedReader br;
	StringTokenizer st;

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

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

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

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