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:
q = int(input())

powers = [1]
for i in range(50):
    powers.append(powers[-1]*2)
    
for _ in range(q):
    a,b,m = [int(x) for x in input().split()]
    if a == b:
        print(1,a)
    else:
        if m == 1:
            good = False
            for r in range(50):
                if powers[r]*(a+1) > b:
                    break
                else:
                    if powers[r]*(a+1) == b:
                        good = True
                        power = r
                        break
            if good:
                print(power+2, end = ' ')
                print(a,end= ' ')
                for j in range(r):
                    print((a+1)*powers[j], end = ' ')
                print((a+1)*powers[r])
                    
            else:
                print(-1)
        else:
            terms = 0
            for r in range(50):
                if powers[r]*(a+1) > b:
                    break
                else:
                    if powers[r]*(a+m) >= b:
                        terms = r+2
                        break
                
            if terms == 0:
                print(-1)
            else:
                components = terms-1
                p = components-1
                X = b-powers[p]*a
                C = [0]
                for q in range(components):
                    if q != components-1:
                        C.append(min(X//powers[p-q-1],m))
                        X -= powers[p-q-1]*C[-1]
                        if q < components-1 and X < powers[p-q-1]:
                            X += powers[p-q-1]
                            C[-1] -= 1
                    else:
                        C.append(X)
                    
                T = [a,a+C[1]]
                for l in range(1,components):
                    T.append(T[-1]*2+C[l+1]-C[l])
                print(terms, end = ' ' )
                for e in T:
                    if e != T[-1]:
                        print(e,end = ' ')
                    else:
                        print(e)