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?

在黑板上，鲍勃用十进制（即位值记数法中的底数为 $10$）写下了 $n$ 个正整数，它们的和为 $s$。爱丽丝看到了黑板，但不小心将黑板上的数字误认为是十一进制（base-$11$）整数，并在十一进制下将它们相加。

鲍勃应在黑板上写下哪些数字，才能使爱丽丝计算出的和尽可能大？

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 $10$).

输入包含多个测试用例。第一行包含一个整数 $t$（$1 \leq t \leq 100$），表示测试用例的数量。随后是各测试用例的描述。

每个测试用例仅有一行，包含两个整数 $s$ 和 $n$（$1 \leq s \leq 10^9$；$1 \leq n \leq \min(100, s)$），分别表示黑板上所有数字的总和与数字的个数。数字 $s$ 和 $n$ 均以十进制（基数为 $10$）给出。

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.

对于每个测试用例，输出 $n$ 个正整数——即 Bob 应写在黑板上的数字，使得 Alice 的和尽可能大。如果存在多个答案，输出任意一个即可。

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 $132_{10}$.

在第一个测试用例中，$70_{10} + 27_{10} = 97_{10}$，而爱丽丝的和为

$$70\_{11} + 27\_{11} = 97\_{11} = 9 \\cdot 11 + 7 = 106\_{10}.$$

（此处 $x_b$ 表示以 $b$ 为进制的数 $x$。）可以证明，爱丽丝无法得到大于 $106_{10}$ 的和。

在第二个测试用例中，鲍勃只能在黑板上写一个数，因此他必须写 $17$。

在第三个测试用例中，$3_{10} + 4_{10} + 100_{10} + 4_{10} = 111_{10}$，而爱丽丝的和为

$$3\_{11} + 4\_{11} + 100\_{11} + 4\_{11} = 110\_{11} = 1 \\cdot 11^2 + 1 \\cdot 11 = 132\_{10}.$$

可以证明，爱丽丝无法得到大于 $132_{10}$ 的和。