A15715. Taisia and Dice

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.

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.

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.