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}$$$.