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().strip())
for i in range(q):
    a,b,m=map(int,input().strip().split())
    p=a+1
    q=a+m
    c=1
    pos=0
    q=0
    if(b==a):
        print(1,a)
    else:
        while(b/c>a+m):
            c=c<<1
            q+=1
        if(b/c>=a+1):
            pos=1
        if(pos):
            #print(b,c)
            d=(c*(a))
            l=[1 for i in range(q+1)]
            ll=[ii-1 for ii in range(q+1)]
            ll[0]+=1
            s=b-d-c
            pp=q
            #print(s,pp)
            while(s>0):
                l[pp]+=min((s//pow(2,ll[pp])),m-1)
                s=s-((l[pp]-1)*pow(2,ll[pp]))
                pp-=1
            ss=a
            po=a
           # print(l)
            print(q+2,end=" ")
            print(ss,end=" ")
            for i in range(q+1):
                ss=po+l[q-i]
                print(ss,end=" ")
                po=po+ss
            print()

        else:
            print(-1)