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:
//package com.algo.rishabh.arrays;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class CuteSequences {

    public static void main(String[] args) throws IOException {
        InputStreamReader isr = new InputStreamReader(System.in);
        BufferedReader br = new BufferedReader(isr);

        int T = Integer.parseInt(br.readLine());
        while (T > 0) {
            String str[] = br.readLine().split(" ");
            long a = Long.parseLong(str[0]);
            long b = Long.parseLong(str[1]);
            long m = Long.parseLong(str[2]);

            if (a == b) {
                System.out.println("1 " + a);
            } else {
                int powerOfTwoExp = (int) (Math.log(b / a) / Math.log(2));
                long powerOfTwo = 1L << powerOfTwoExp; //2^powerOfTwoExp
                long sumOfXs = powerOfTwo * a;//sum of all previous elements for the last element
                int n = powerOfTwoExp + 2;//number of elements

                boolean flag = false;

                while (sumOfXs >= a) {

                    long sumOfRs = b - sumOfXs;
                    long commonRDivisor = sumOfRs / (1L << (n - 2)); //common r divisor
                    long remainingRsum = sumOfRs % (1L << (n - 2)); //remaining r sum

                    long valueOfR = commonRDivisor + (remainingRsum > 0 ? 1 : 0);

                    if (commonRDivisor > 0 && valueOfR <=m) {

                        //we have to evaluate remaining sum
                        System.out.print(n + " " + a + " ");
                        long sumOfPrevElements = a;
                        for (int i = 2; i <= n - 1; i++) {
                            long currentRCoefficient = 1L << (n - 1 - i);
                            long currentElement =
                                sumOfPrevElements + commonRDivisor
                                    + remainingRsum / currentRCoefficient;

                            System.out.print(currentElement + " ");
                            sumOfPrevElements += currentElement;
                            remainingRsum = remainingRsum % currentRCoefficient;
                        }

                        System.out.println(b);

                        flag = true;
                        break;
                    }

                    n--;
                    sumOfXs /= 2;

                }

                if (!flag) {
                    System.out.println(-1);
                }


            }

            T--;
        }
    }
}