You have a keyboard with the numeric keys $$$0,1,2,\cdots,9$$$.
For any positive integer $$$m$$$, you can obviously always type a positive integer that is a multiple of $$$m$$$.
Now, $$$k$$$ of your positive integer keys have been knocked off, but you still want to type a positive integer that is a multiple of $$$m$$$.
Each test contains multiple test cases. The first line contains an integer $$$T(1 \leq T \leq 5 \times 10^4)$$$, representing the number of test cases.
For each test case:
The first line contains two positive integers $$$m, k(1 \leq m \leq 10^7, 0 \leq k \leq 9)$$$, indicating that after $$$k$$$ keys are removed, you need to press a sequence of keys to produce a positive integer that is a multiple of $$$m$$$.
The second line gives $$$k$$$ distinct positive integers $$$p_i(1\leq p_i \leq 9)$$$, representing the removed keys.
For each test case:
If a solution exists, output your operations as a sequence of multiple "press digit $$$a$$$ for $$$b$$$ times" operations: The first line outputs an integer $$$n$$$, where $$$1 \leq n \leq 100$$$, representing the number of operations required.
The next $$$n$$$ lines each output two integers $$$a,b$$$ ($$$0 \leq a \leq 9, 1 \leq b \leq 10^{18}$$$), representing one operation "press digit $$$a$$$ for $$$b$$$ times".
If no solution exists, output a single line containing $$$-1$$$.
2 37 7 2 3 5 6 7 8 9 7 9 1 2 3 4 5 6 7 8 9
2 1 3 0 1 -1
For the first test case in the example, the positive integer output is $$$1110$$$. Since $$$1110 = 37 \times 30$$$, it is a multiple of $$$37$$$.
