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Problems

Fraction

Fraction

Time limit 1 second
Memory limit 64 MiB

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 data

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 data

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

Input example #1
10 5 2
1 2 8
8780 1 29
2794 6083 23
157 7 19
1 12 10
0 0
Output example #1
10
0.4
ACM
0.(ACM)
13.(82DAG5)
0.08(3)
Author Dmitry Zhukov
Source Ural SU and Orel STU Contest. Petrozavodsk Summer Session, August 2006