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:
t=int(input())
def r(i,m):
    return 1<<i,m*(1<<i)
def bis(i,e,m):
    if i==0:
        return e
    mn=(1<<(i-1))
    e-=mn
    mlt=(1<<(i-1))
    l,r=1,m
    if r*mlt<=e:
        return r
    while r-l>1:
        m=(r+l)//2
        if m*mlt<=e:
            l=m
        else:
            r=m
    return l
for _ in range(t):
    s,e,m=list(map(int,input().split()))
    ee=e
    if e==s:
        print('1 {}'.format(s))
        continue
    for i in range(100):
        if s*(1<<i)+(1<<i)*m >= e:
            ii=i
            break
    if s*(1<<i)+(1<<i)>e:
        print(-1)
        continue
    print(i+2,end=' ')
    e-=s*(1<<i)
    ans=[s]
    while i>=0:
        x=bis(i,e,m)
        if i>0:
            e-=x*(1<<(i-1))
        ans.append(x)
        i-=1
    cur=s
    # print('ans: ',ans)
    for j in range(ii+1):
        print(cur,end=' ')
        cur=cur*2-ans[j]+ans[j+1]
    print(cur)
    # print(ans)