DWITE Online Computer Programming Contest, November 2010, Problem 4

In math class, writing fractions in their decimal form was a common task. However, the teachers would usually have you round off the number to a certain number of decimal places. But all fractions have a nice property: in decimal form, they all either terminate or repeat in a pattern. For example, the fraction ~1/10~ terminates, as ~1/10 = 0.1~. However, the fraction ~1/3~ repeats, as ~1/3 = {0.333\dots} = 0.(3)~ (note that the repeated part is parenthesized). Given a fraction, output its decimal form, parenthesizing the cyclic part of the fraction, if such exists.

The input will contain 5 lines, each a pair of integers ~1 \le N < D \le 400~, separated by a single space.

The output will contain 5 lines, the decimal forms of ~N/D~, truncating and parenthesizing the repeating digits, if such is the case.

Note: the answers must match exactly and use the shortest repeating pattern. Since ~D~ is always greater than ~N~, all of the answers are less than ~1.0~.

Sample Input

1 10
1 3
2 7
2 3
6 10

Sample Output

0.1
0.(3)
0.(285714)
0.(6)
0.6

Problem Resource: DWITE