Beautiful Array

Description:

Input:

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 1000$$$). Description of the test cases follows.

The first line of each test case contains integers $$$n$$$, $$$k$$$, $$$b$$$, $$$s$$$ ($$$1 \leq n \leq 10^{5}$$$, $$$1 \leq k \leq 10^{9}$$$, $$$0 \leq b \leq 10^{9}$$$, $$$0 \leq s \leq 10^{18}$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.

Output:

For each test case print $$$-1$$$ if such array $$$a$$$ does not exist. Otherwise print $$$n$$$ non-negative integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \leq a_{i} \leq 10^{18}$$$) — the answer.

Sample Input:

8
1 6 3 100
3 6 3 12
3 6 3 19
5 4 7 38
5 4 7 80
99978 1000000000 100000000 1000000000000000000
1 1 0 0
4 1000000000 1000000000 1000000000000000000

Sample Output:

-1
-1
0 0 19
0 3 3 3 29
-1
-1
0
0 0 0 1000000000000000000

Note:

In the first, the second, the fifth and the sixth test cases of the example it is possible to show that such array does not exist.

In the third testcase of the example $$$a = [0, 0, 19]$$$. The sum of elements in it is equal to 19, the beauty of it is equal to $$$\left ( \left \lfloor \frac{0}{6} \right \rfloor + \left \lfloor \frac{0}{6} \right \rfloor + \left \lfloor \frac{19}{6} \right \rfloor \right ) = (0 + 0 + 3) = 3$$$.

In the fourth testcase of the example $$$a = [0, 3, 3, 3, 29]$$$. The sum of elements in it is equal to $$$38$$$, the beauty of it is equal to $$$(0 + 0 + 0 + 0 + 7) = 7$$$.