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.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.*;
import java.lang.StringBuilder;

public class TestClass
{
    static class Reader
    {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader()
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException
        {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException
        {
            byte[] buf = new byte[1000]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1)
            {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do
            {
                ret = ret * 10 + c - '0';
            }  while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.')
            {
                while ((c = read()) >= '0' && c <= '9')
                {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }
    }

    static int getIndex(int arr[],int val,int r){
        int l=0;
        while(true){
            int m=(l+r)/2;
            if(m==l)
            {
                if(arr[m]<val && arr[m+1]>=val)
                {
                    return m;
                }
                else if(arr[m]<val && arr[m+1]<val)
                {
                    return r;
                }
                else if(arr[m]>=val && arr[m+1]>=val)
                    return m-1;
//             if(m==0)
//             {
//                    return -1;
//             }
//             else
//                 return r-1;
            }
            if(arr[m]<val && arr[m+1]>=val)
            {
                return m;
            }
            else if(arr[m]>=val)
            {
                r=m;
            }
            else
            {
                l=m;
            }
        }

    }
    static void printArray(int a[]){
        int length=a.length;
        for(int i=0;i<length;i++){
            System.out.print(a[i]+" ");
        }
        System.out.println();
    }
    public static void main(String[] args) throws IOException
    {
        Reader s=new Reader();
        int q=s.nextInt();
        outer: for(int q0=0;q0<q;q0++) {
            long a = s.nextLong();
            long b = s.nextLong();
            long m = s.nextLong();
            if(a==b)
            {
                System.out.println(1+" "+a);
                continue;
            }
            if(a>b)
            {
                System.out.println("-1");
                continue;
            }
            long div = b / a;
            int i = (int) (Math.log(div) / Math.log(2));
            if (b > Math.pow(2, i + 1) * a) {
                i = i + 1;
            } else if (b > Math.pow(2, i) * a) {
                i = i;
            } else if (b > Math.pow(2, i - 1) * a)
                i = i - 1;
            int i1=i;
            for (i=0; i <=i1; i++) {
                long remain = b - (long) Math.pow(2, i) * a;
                int rounds = i + 2;
                int terms = i + 1;
                long coeff[] = new long[terms];
                coeff[terms - 1] = 1;
                int power = 0;
                for (int j = terms - 2; j > -1; j--) {
                    coeff[j] = (long) Math.pow(2, power);
                    power++;
                }
                long min = (long) Math.pow(2, power);
                long max = min * m;
                if (!(remain >= min && remain <= max)) {
                    //System.out.println("-1");
                    if(i==i1)
                        System.out.println("-1");
                    continue;
                }
                long value[] = new long[terms];
                Arrays.fill(value, m);
                long todel = max - remain;
                for (int j = 0; j < terms; j++) {
                    long delt = todel / coeff[j];
                    if (delt + 1 <= m) {
                        value[j] -= delt;
                        todel -= delt * coeff[j];
                    } else {
                        value[j] = 1;
                        todel -= (m - 1) * coeff[j];
                    }
                    if (todel == 0) {
                        break;
                    }
                }
                System.out.print(rounds + " " + a + " " + (a + value[0]) + " ");
                long ans = a + value[0];
                for (int j = 1; j < terms; j++) {
                    ans = (ans * 2) - value[j - 1] + value[j];
                    System.out.print(ans + " ");
                }
                System.out.println();
                continue outer;
            }
        }

    }
}