D. Expression Evaluation Error
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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?

Input

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 $10$).

Output

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.

Example
Input
6
97 2
17 1
111 4
100 2
10 9
999999 3

Output
70 27
17
3 4 100 4
10 90
1 1 2 1 1 1 1 1 1
999900 90 9

Note

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 $132_{10}$.