Sum and Difference
Description
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:
- $l\le a_i\le r$;
- For all $i(1 \leq i \leq n-1)$,$|a_i-a_{i+1}|$ is prime;
- 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.
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 $n,l,r(2 \le n\le 1000,1 \le l\le r\le 2000)$.
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 $−1$.
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 $−1$.
3
3 1 4
5 1 4
5 10 20
1 4 2
-1
10 15 12 19 14