# UVa 10812

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## 10812 - Beat the Spread![edit]

## Summary[edit]

This is a pretty standard formula manipulation math problem.

## Explanation[edit]

Given the sum of *a* and *b*, and the difference of *a* and *b*, find *a* and *b*. First, make sure the difference is not greater than the sum, since this would imply one of them is negative. Without a lost of generality, assume . We get

and .

Solving for *a* in terms of *b*, we get:

plugging it into the latter equation:

or

We then solve for *b* numerically and plug it into one of the formulas to get *a*. All that's left is to check that *a* and *b* are both non-negative, and we're done.

NOTE: Check that and are both divisible by 2. :-)

## Implementations[edit]

## Input[edit]

8 40 20 20 40 1 5 100 6 12 61 51 61 123 512 63 1

## Output[edit]

30 10 impossible impossible 53 47 impossible impossible impossible 32 31