Time Limit: 1500 ms Memory Limit: 10000 KiB
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.
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.
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.
3 7 345 800 112 990 53 122 0 0
.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.