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:
import math
import re
import sys
from collections import defaultdict
from heapq import heappush, heappop
from fractions import gcd

def read(type = int):
  return type(input())
  
def read_list(type = int, split = ' ', F = None):
  if F:
    return map(lambda x: F(type(x)), raw_input().split(split))
  return map(type, input().split(split))

def read_list_of_list(N, type = int, split = ' ', F = None):
  return [read_list(type, F = F) for _ in range(N)]


def solve():
  a,b,m = read_list()
  if a==b:
    return "1 %d" %a
  e = 0
  while a*2**e+m*2**e<b:
    e += 1
  if a*2**e>=b:
    return -1
  z = b-a*2**e-2**e
  if z<0:
    return -1
  X = [1]*(e+1)
  i = 0
  while z:
    if e > 0:
      e -= 1
    k = min(z//2**e, m-1)
    X[i] += k
    i += 1
    z -= k*2**e
#  print(X,z)
  R = [a]
  i = 0
#  X += [0]*3
#  print(X)
  while a<b:
    a = sum(R)+X[i]
    R += [a]
    i += 1
  return " ".join(map(str, [len(R)]+R))
      
q = read()
for _ in range(q):
  print(solve())