Write a program in Java,

$(1)$ "fibonacci" $-$ Takes as argument a single non$-$zero, positive integer and prints the fibonacci series up to the highest fibonacci number that is smaller or equal to the input

argument. The output should be in ascending order with a single space character separating each integer.

Eg: If $"15"$ is the input argument, the output would be $"011235813"."15"$ is not a fibonacci number so we print up to the highest fibonacci number that is less than or equal

to $"15"$; in this case that is $"13".$

Eg: If $"21"$ is the input argument, the output would be $"01123581321"."21"$ is a fibonacci number, so we print all the fibonacci numbers up to and including $"21".$

Eg: If $"1"$ is the input argument, the output would be $"011".$

If the input argument is anything other than a positive, non$-$zero integer, you must print the string "error".

Eg: If $"-6"$ is the input argument, output must be "error".

Eg: If "helloworld" is the input argument, output must be "error"

Eg: If $"0"$ is the input argument, the output must be "error".

$(2)$ "overlap" $-$ Takes as argument a list of ranges and determines whether any two ranges overlap. If there is any overlap, it prints "true", otherwise it prints "false".

A range is given in the form $"$a$,$b$",$ where a and b are both integers and where a $<=$ b$.$ Note that a and b can be negative, zero or positive. A list of ranges is a sequence of

ranges separated by a single space character $("")$: $"$a$,$b x$,$y j$,$k$".$ Two ranges overlap if they partially, or fully cover the same set of integers. For example: $"3,6"$ and $"5,9"$

overlap because they both include $5$ and $6.$ Similarly, $"8,176"$ and $"6,11"$ also overlap because they both include $8,9,10$ and $11.$ On the other hand, $"17,17"$ and $"-5,4"$ do not

overlap because they do not share any integers.

If you encounter a malformed range, you must print "error". A malformed range, $"$a$,$b$",$ is one where either a or b are not integers or where a $>$ b$.$

For example, the following ranges are all malformed $"17,4","-1,-5",$ "five,$9","1,$$$*$$$",$ "hello,world".

The "overlap" function is guaranteed to be given a list of at least two intervals, therefore you need not worry about an empty list or a single

range as arguments.

Eg: Given $"17,2001,217,178,9"$ as input, the function would print "true" because $"17,200"$ and $"17,17"$ overlap.

Eg: Given $"8,994,71,3"$ as input, the function would print "false" because no ranges overlap.

Eg: Given $"4,8$ dd$,5"$ as input, the function would print "error" because $"$dd$,5"$ is a malformed range.

$(3)$ "stats" $-$ Takes no arguments and prints the number of calls to "fibonacci" and "overlap" $($in that order$)$ as two integers, on a single line, separated by a single space

character $("").$

Eg: If "fibonacci" is called three times, and "overlap" is called twice, the output should be $"32"$

The input to your program will be given on stdin and will consist of one function call per line. Each line starts with a string $("$fibonacci$",$

"overlap" or "stats"$),$ indicating which function is being called. Following the function name, there will be a single space character $(""),$

after which the input to the function $($if any$)$ is presented. If "stats" is called, it will always be the last function call.

$-----------------------$

Sample input:

fibonacci $21$

overlap $8,994,71,3$

fibonacci $0$

fibonacci $15$

overlap $1,310,17-10,02,4$

stats

Sample output:

$01123581321$

false

error

$011235813$

true

$32$

$-----------------------$