Good array#12291
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Good array

1 second
256 megabytes
Easy

Today, Rasul's teacher — Ruslan, gave a problem to him. In the problem, you are given , , . Teacher Ruslan says the array is called good if and only if these two conditions are correct:

\begin{cases}\gcd(a_1, a_2, ..., a_n) = x \\ \text{lcm}(a_1, a_2, ..., a_n) = y \end{cases}

In this problem, denotes the greatest common divisor, denotes the least common multiple.

Now, Ruslan's teacher wants the lexicographical minimum good array. Help Rasul to find an array that holds the condition above.

Input

First line contains a single integer (1\le t \le 10^4), the number of test cases.

Each test case contains three integers , , (1 \le n \le 2\cdot10^5, 1 \le x \le 10^9, 1 \le y \le 10^9) — the length of array , the greatest common divisor and the least common multiple of the array respectively.

It is guaranteed that the sum of across all test cases does not exceed 2\cdot10^5.

Output

For each test case, print the lexicographically minimum good array, or if no such array exists.

Examples

Example 1

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Scoring

  1. Subtask ( points): (x=y).

  2. Subtask ( points): No additional constraints