D. Sum and Difference
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given three numbers $$$n,l,$$$ and $$$r$$$.

Your task is to construct an array $$$a$$$ with $$$n$$$ integers which satisfies the following conditions:

  1. $$$l\le a_i\le r$$$;
  2. For all $$$i(1 \leq i \leq n-1)$$$,$$$|a_i-a_{i+1}|$$$ is prime;
  3. For all $$$i(1 \leq i \leq n-1)$$$,$$$(a_i+a_{i+1})$$$ is distinct.

If this is impossible, return $$$-1$$$.

NOTE: 0 and 1 are both not prime numbers.

Input

The first line contains a single integer $$$t(1 \le t\le 1000)$$$ — the number of test cases.

The only line of each test case contains three numbers $$$n,l,r(2 \le n\le 1000,1 \le l\le r\le 2000)$$$.

Output

For each test case, output $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$.

If there are multiple solutions, print any of them.

If there is no solution, print a single integer $$$−1$$$.

Example
Input
3
3 1 4
5 1 4
5 10 20
Output
1 4 2
-1
10 15 12 19 14