There are two numbers, a and b. It is required to calculate the value a/b and write it in the kbased 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 kbased 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.
Sample
input  output 

10 5 2
1 2 8
8780 1 29
2794 6083 23
157 7 19
1 12 10
0 0
 10
0.4
ACM
0.(ACM)
13.(82DAG5)
0.08(3)

Problem Author: Dmitry Zhukov
Problem Source: Ural SU and Orel STU Contest. Petrozavodsk Summer Session, August 2006