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 PYTHON):

Solution:
from collections import deque, namedtuple
import random
import time

seed = int(time.time())
random.seed(seed)

def solve(a, b, m):
    if a == b:
        return "1 %d" % a

    for k in range(2, 51):
        fk = b - 2**(k-2)*a
        min_fk = 2**(k-2)
        max_fk = m*min_fk
        #print k, min_fk, max_fk
        if fk < min_fk:
            #print 'fk lt min_fk'
            continue
        if fk > max_fk:
            #print 'fk gt max_fk'
            continue
        rs = [1 for _ in range(k)]
        rs[0] = 0

        b2 = fk - min_fk
        #print b2
        rs[-1] += min(m-1, max(b2, 0))
        b2 -= (rs[-1] - 1)
        #print b2
        #for r_ix in range(k-2, 0, -1):
        #    rs[r_ix] += max(0, min(b2 // (2**(k-2-r_ix)), m-1))
        #    b2 -= (rs[r_ix] - 1) * 2**(k-2-r_ix)
        #    print b2
        for r_ix in range(1, k-1):
            rs[r_ix] += max(0, min(b2 // (2**(k-2-r_ix)), m-1))
            b2 -= (rs[r_ix] - 1) * 2**(k-2-r_ix)
            #print b2
        #print 'rs:', rs
        xs = [a]
        xacc = a
        for i in range(1, k):
            xs.append(xacc + rs[i])
            xacc += xs[-1]
        #print 'xs:', xs
        if xs[-1] != b:
            continue
        return "%d %s" % (k, ' '.join([str(x) for x in xs]))
    return "-1"

def main():
    q = int(raw_input().strip())
    for _ in range(q):
        xs = [int(x) for x in raw_input().strip().split()]
        print solve(*xs)

if '__main__'==__name__:
    main()