## Multiples

Points: 1 (partial)
Time limit: 2.0s
Memory limit: 512M

Author:
Problem type

Imagine you are still a lowly high-school student (apologies to the lowly high-school students competing). You are bored in maths class (purely hypothetically). To amuse yourself, you are playing a game. The games works as follows. You want to find the largest non-negative multiple of a positive integer $$X$$ such that the number of digits (in base 10) is exactly $$D$$. Several of your friends have started playing. So you can shame them and their families, you have decided to write a program to play the game.

#### Input Specification

The first line of input contains an integer, $$T$$ ($$1 \leq T \leq 100$$), the number of test cases. The next $$T$$ lines each define a test case. A test case is defined by a line containing two space separated integers $$X$$ and $$D$$.

#### Output Specification

Display a single line for each test case. The largest possible multiple. If there is no valid multiple, display -1.

#### Bounds

Note this problem includes sub-problems of increasing difficulty worth different numbers of points:

• 20 points: $$1 \leq X \leq 1000$$ and $$1 \leq D \leq 4$$
• 100 points: $$1 \leq X \leq 10^9$$ and $$1 \leq D \leq 10$$

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7 3
11 2
93 4
99 1

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