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 PYTHON3):

Solution:
N = int(input())
for _ in range(N) :
    a, b, m = list(map(int, input().split()))

    m -= 1
    if a == b:
        print('1 '+ str(a))
        continue

    c = a
    d = 1
    f = False
    r = []
    while (b-(1<<(d-1))-c) >= 0:
        if (b-(1<<(d-1))-c) <= (m<<(d-1)):
            rem = b-(1<<(d-1))-c
            for i in range(d-2, -1, -1) :
                r.append(min(rem>>i, m))
                rem -= min(rem>>i, m)*(1<<i)
            r.append(rem)
            assert 0 <= rem <= m
            f = True
            break
        else:
            d += 1
            c *= 2
    if f:
        cs = a
        tr = [str(d+1), str(a)]

        for i in range(d) :
            tr.append(str(cs+r[i]+1))
            cs = cs+cs+r[i]+1
        print(' '.join(tr))
    else :
        print(-1)