OnlineJudge 3 现已推出。点此体验新版：Expanding Fractions | SDUT OnlineJudge

### Expanding Fractions

Time Limit: 1500 ms
Memory Limit: 10000 KiB

#### Problem Description

In this problem you are to print the decimal expansion of a quotient

of two integers. As you well know, the decimal expansions of many

integer quotients result in decimal expansions with repeating

sequences of digits. You must identify these. You will print the

decimal expansion of the integer quotient given, stopping just as the

expansion terminates or just as the repeating pattern is to repeat

itself for the first time. If there is a repeating pattern, you will

say how many of the digits are in the repeating pattern.

#### Input

There will be multiple input instances, each instance consists of two

positive integers on a line. The first integer represents the

numerator of the fraction and the second represents the denominator.

In this problem, the numerator will always be less than the

denominator and the denominator will be less than 1000. Input

terminates when numerator and denominator are both zero.

#### Output

For each input instance, the output should consist of the decimal

expansion of the fraction, starting with the decimal point. If the

expansion terminates, you should print the complete decimal expansion.

If the expansion is infinite, you should print the decimal expansion

up to, but not including the digit where the repeated pattern first

repeats itself. For instance, 4/11 = .3636363636..., should be printed

as .36. (Note that the shortest repeating pattern should be found. In

the above example, 3636 and 363636, among others, are repeating

patterns, but the shortest repeating pattern is 36.) Since some of

these expansions may be quite long, multiple line expansions should

each contain exactly 50 characters on each line (except the last line,

which, of course, may be shorter) | that includes the beginning

decimal point. (Helpful hint: The number of digits before the pattern

is repeated will never be more than the value of the denominator.)

On the line immediately following the last line of the decimal

expansion there should be a line saying either "This expansion

terminates.", or "The last n digits repeat forever.", where n is the

number of digits in the repeating pattern.

Output for each input instance (including the last input instance)

should be followed by a blank line.

#### Sample Input

3 7 345 800 112 990 53 122 0 0

#### Sample Output

.428571 The last 6 digits repeat forever. .43125 This expansion terminates. .113 The last 2 digits repeat forever. .4344262295081967213114754098360655737704918032786 885245901639 The last 60 digits repeat forever.