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:
# https://codeforces.com/contest/1166/problem/D
def creat_r(X, k, m, p):
    q = X // p[k]
    r = X %  p[k]
    
    R = []
    for _ in range(k+1):
        R.append(q)
        
    s = bin(r)[2:]
    for i in range(1, len(s)+1):
        if s[-i] == '1':
            R[-(i+1)] += 1
       
    return R

i = 1
p = [1]
for _ in range(50):
    i*=2
    p.append(i)
    
T   = int(input())
ans = []
for _ in range(T):
    a, b, m = map(int, input().split())
    if a == b:
        print(1, a)
        continue
    
    flg = False
    for i in range(50):
        if p[i] * a  >= b: break
    
        k = i
        X = b - (p[i] * a)
    
        if X >= p[k] and X <= p[k]*m:
            flg = True
            R   = creat_r(X, k, m, p)
            sR  = 0 
            A   = [a]
        
            for _ in range(k+1):
                A.append(p[_]*a+sR+R[_])
                sR += sR + R[_] 
            
            print(len(A), end=' ')
            for x in A:
                print(x, end=' ')
            print()
            break
        
        
    if flg == False:
        print(-1)