C. Cave & Tommy
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Tommy went to the jungle. He has found a cave and in the cave, he has found a cage. There is divine water in the cage. The divine water has a special power. Once you drink the water you'll become meritorious. As Tommy is not good at his studies, he wants to drink water to become a meritorious student. But he can't drink the water until he opens the cage. The cage has a display, some buttons, and a lock system. There are twelve buttons. One "Yes" button and one "No" button. The rest of the buttons are digit buttons $$$(0-9)$$$. The cage is locked with a special system.

The display shows three integers $$$x, l, r$$$. The integer $$$x$$$ is good if there exists three integers $$${a, b, c}$$$ such that,

  • $$${l \le a \lt b \lt c \le r}$$$ where $$${2 \le r-l \le 100}$$$
  • $$${a \times b \times c = x}$$$

To open the cage first he has to determine whether the number $$$x$$$ is good or not. If the number is good then he will press the "Yes" button and then he will type the numbers $$$a, b, c$$$. Otherwise, he will press the "No" button. As mentioned above, he is not good at his studies. So he needs your help. Help him to get the divine water.

Input

Each test consists of multiple test cases. The first line contains a single integer t $$$(1 \le t \le 100)$$$ — the number of test cases. Description of the test cases follows.

Each test case contains three integers $$$x(1 \le x \le 10^{9}), l, r(1 \le l \lt r \le 1000, 2 \le r-l \le 100)$$$ in a line.

Output

For each test case, output $$$−1$$$ if the number is not good.

Otherwise, output three integers $$$a,b,c$$$.

If there are several solutions, output any of them.

Example
Input
5
138 1 53
100 1 100
8 2 6
30 2 10
23 12 19
Output
2 3 23
2 5 10
-1
2 3 5
-1