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 get_r_list(a, b, m):
    k = 2
    two_power_k = 1
    isMatch = False

    if a == b:
        return 1, []

    while True:
        if b <= two_power_k * (a + 1):
            isMatch = True
            break

        if k == 50:
            break


        k += 1
        two_power_k *= 2

    isDone = False

    if isMatch and b < two_power_k * (a + 1):
        k -= 1
        two_power_k = int(two_power_k / 2)


    gap = b - two_power_k * (a + 1)

    two_power_k = int(two_power_k / 2) # 2^k-3
    r_list = []

    if b == two_power_k * (a + 1) * 2:
        isDone = True
        for i in range(1, k - 1):
            r_list.append(0)

    while two_power_k != 0:
        # print("two: ", end="")
        # print(two_power_k)
        if gap >= two_power_k:
            index_r = 0

            gap_divide = int(gap / two_power_k)

            if gap_divide > m - 1:
                index_r = m - 1
            else:
                index_r = gap_divide

            gap = gap - two_power_k * index_r
            r_list.append(index_r)

            two_power_k = int(two_power_k / 2)
        else:
            two_power_k = int(two_power_k / 2)
            r_list.append(0)


    if gap == 0:
        isDone = True
        r_list.append(0)

    else:
        if gap <= m - 1:
            isDone = True
            r_list.append(gap)
        else:
            isDone = False

    if isDone:
        return k, r_list

    else:
        return -1, r_list

    # print(k)
    # print(r_list)


def cute_sequence(a, b, m):
    k, r_list = get_r_list(a, b, m)

    if k == -1:
        print(k)
        return

    if k == 1:
        print(1, end=" ")
        print(b)
        return

    sequence_list = []
    sequence_list.append(a)

    sequence_list.append(a + r_list[0] + 1)

    for i in range(2, k):
        next_a = 2 * sequence_list[i - 1] + r_list[i - 1] - r_list[i - 2]
        sequence_list.append(next_a)
    print(k, end=" ")

    for ele in sequence_list:
        print(ele, end=" ")
    print()
    return



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