Fraction — Eolymp

Input

The input consists of several tests (no more than $100$ ). The tests are separated by line breaks. Each test contains three numbers: $1 \leq a \leq 10000$ 1 \leq a \leq 10000, $1 \leq b \leq 10000$ 1 \leq b \leq 10000, $2 \leq k \leq 36$ 2 \leq k \leq 36. The last line contains two zeros.

Output

For each test, output a line containing the representation of $\frac{a}{b}$ \frac{a}{b} in base $k$ . The integer part should be separated from the fractional part by a point. If $\frac{a}{b}$ \frac{a}{b} is an integer, the point should not be printed. The representation must not contain insignificant zeros. If $\frac{a}{b}$ \frac{a}{b} is a periodic fraction, its period should be enclosed in parentheses.

Examples

Example 1

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