#B4008. Restoring the True Attributes

    ID: 11665 Type: Default 1000ms 256MiB

Restoring the True Attributes

Restoring the True Attributes

In Little A's kingdom, there are three attributes whose sum is exactly \(10000\). However, the values observed by Little A are not the true attributes. Instead, he sees the following:

  • The first attribute is shown after being multiplied by \(10\).
  • The second attribute is shown after being divided by \(10\).
  • The third attribute is hidden.

Let the true values of the three attributes be \(a\), \(b\), and \(c\) respectively. Based on the observations:

\[ \begin{aligned} 10a &= \text{observed first value},\\ a/\, \text{?} &\quad \text{(Note: See below)} \\ 0.1b &= \text{observed second value}. \end{aligned} \]

Actually, the transformations are as follows:

  • Observed first value \(A' = 10 \times a\) → \(a = A'/10\).
  • Observed second value \(B' = b/10\) → \(b = B' \times 10\).

Since \(a + b + c = 10000\), the hidden third attribute is computed as \(c = 10000 - a - b\). Given the observed values \(A'\) and \(B'\), compute the true values of \(a\), \(b\), and \(c\).

inputFormat

The input consists of two numbers separated by spaces:

  • The first number represents the observed value of the first attribute \(A'\) (which is \(10 \times a\)).
  • The second number represents the observed value of the second attribute \(B'\) (which is \(b/10\)).

outputFormat

Output the three true attribute values \(a\), \(b\), and \(c\) separated by a space. Make sure the values satisfy \(a + b + c = 10000\).

sample

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