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 PYTHON):

Solution:
import fileinput
def D(a):print(a)
def S(s,I):return int(s.split(" ")[I])
def TM(I):
    if(I==1):return 1
    return 1<<(I-2)
def XX(I):
    S=0
    for i in xrange(1,I):S+=TM(i)
    return S
def go(l):
    a=S(l,0)
    b=S(l,1)
    m=S(l,2)
    if(a==b):
        D("1 "+str(a))
        return
    for i in range(47):
        x=1<<i
        t=b-x*a
        if(t<1 or m*x<t or x>t):continue
        s=str(i+2)+" "+str(a)
        w=a
        for j in range(i+1):
           I=i+1-j
           r=min(m,(t-XX(I))/TM(I))
           #D("["+str(t)+"]: "+str(I)+" "+str(TM(I))+" "+str(XX(I))+" ==> "+str(r))
           t-=r*XX(I)
           a=w+r
           w+=a
           s+=" "+str(a)
        D(s)
        return
    D(-1)

def main():
    z=0
    for l in fileinput.input():
        z+=1
        if(z<2):continue
        go(l)
main()