Fraction

There are two numbers, a and b. It is required to calculate the value a/b and write it in the k-based number system.

Input

The input consists of several tests (not more than 100) separated by a line break. Each test consists of three integers 1 ≤ a ≤ 10000, 1 ≤ b ≤ 10000, 2 ≤ k ≤ 36. There are two zeros in the last line.

Output

For each test, output a line containing the representation of the number a/b in the k-based number system. The integer part must be separated from the fractional part by a point. If the number a/b is whole, then there should be no point. The output must not contain insignificant zeros. If the fraction a/b is periodic, then its period must be given in parentheses.

Examples