B. Taisia and Dice
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Taisia has $$$n$$$ six-sided dice. Each face of the die is marked with a number from $$$1$$$ to $$$6$$$, each number from $$$1$$$ to $$$6$$$ is used once.

Taisia rolls all $$$n$$$ dice at the same time and gets a sequence of values $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 6$$$), where $$$a_i$$$ is the value on the upper face of the $$$i$$$-th dice. The sum of this sequence is equal to $$$s$$$.

Suddenly, Taisia's pet cat steals exactly one dice with maximum value $$$a_i$$$ and calculates the sum of the values on the remaining $$$n-1$$$ dice, which is equal to $$$r$$$.

You only know the number of dice $$$n$$$ and the values of $$$s$$$, $$$r$$$. Restore a possible sequence $$$a$$$ that fulfills the constraints.

Input

The first line contains the integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of testcases.

Each testcase is given on a separate line and contains three integers $$$n$$$, $$$s$$$, $$$r$$$ ($$$2 \le n \le 50$$$, $$$1 \le r < s \le 300$$$).

It is guaranteed that a solution exists.

Output

For each testcase, print: $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ in any order. It is guaranteed that such sequence exists.

If there are multiple solutions, print any.

Example
Input
7
2 2 1
2 4 2
4 9 5
5 17 11
3 15 10
4 4 3
5 20 15
Output
1 1
2 2 
1 2 2 4
6 4 2 3 2
5 5 5
1 1 1 1
1 4 5 5 5