CF1567D.Expression Evaluation Error

On the board, Bob wrote $n$ positive integers in base $10$ with sum $s$ (i. e. in decimal numeral system). Alice sees the board, but accidentally interprets the numbers on the board as base- $11$ integers and adds them up (in base $11$ ).

What numbers should Bob write on the board, so Alice's sum is as large as possible?

The input consists of multiple test cases. The first line contains an integer $t$ ( $1 \leq t \leq 100$ ) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $s$ and $n$ ( $1 \leq s \leq 10^9$ ; $1 \leq n \leq \min(100, s)$ ) — the sum and amount of numbers on the board, respectively. Numbers $s$ and $n$ are given in decimal notation (base $10$ ).

For each test case, output $n$ positive integers — the numbers Bob should write on the board, so Alice's sum is as large as possible. If there are multiple answers, print any of them.

In the first test case, $70_{10} + 27_{10} = 97_{10}$ , and Alice's sum is $$$$70_{11} + 27_{11} = 97_{11} = 9 \cdot 11 + 7 = 106_{10}. $$ (Here $x\_b$ represents the number $x$ in base $b$ .) It can be shown that it is impossible for Alice to get a larger sum than $106\_{10}$ .

In the second test case, Bob can only write a single number on the board, so he must write $17$ .

In the third test case, $3\_{10} + 4\_{10} + 100\_{10} + 4\_{10} = 111\_{10}$ , and Alice's sum is $$ 3_{11} + 4_{11} + 100_{11} + 4_{11} = 110_{11} = 1 \cdot 11^2 + 1 \cdot 11 = 132_{10}. $$ It can be shown that it is impossible for Alice to get a larger sum than $132\_{10}$$$.