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:
def solve(a, b, m):
    if a == b:
        return [a]

    for _len in range(2, 51):
        l = (a + 1) * (2 ** (_len - 2))
        r = (a + m) * (2 ** (_len - 2))
        if b < l or b > r: continue

        res = []
        res += [a]

        s = a

        for i in range(1, _len-1):
            L = 0
            R = m + 1
            while R - L > 1:
                M = int((L + R) // 2)
                l = (s + s + M + 1) * 2 ** (_len - i - 2)
                r = (s + s + M + m) * 2 ** (_len - i - 2)
                if r < b:
                    L = M
                else:
                    R = M

            x = s + R
            res += [x]
            s += x
        res+=[b]

        return res

tc = int(input())
for _ in range(tc):
    a, b, m = map(int, input().split())
    res = solve(a, b, m)
    if res:
        print(len(res), end=' ')
        for i in res:
            print(i, end=' ')
        print()
    else:
        print(-1)