Write A Program That Constructs Either The Shortest Word Chain: Computer Science Course Work, UOA, New Zealand

Task
Write a program that constructs either the shortest word chain connecting a pair of words from a given list or a chain of a specified length.

The input for this task consists of a file (to be read from stdin) that contains a list of word chain problems (one per line, no blank lines) followed by a blank line, followed by a list of words that can be used (all lower case letters, not necessarily all of the same length). The output, to stdout, should be the (or a) solution to each problem.

If an impossible problem is given, the output should echo the input for that problem, followed by a space and the word impossible. A problem consists either of two words or two words followed by a number. In the first case, the shortest possible chain between them is to be found and in the second case, a chain of exactly the given length (the length of a chain is the total number of words in the chain).
For example with this input file:

cat   cup
cap  cup 4
cat   dog 3
emu kea
flu   covid
car  cat
cat
cup
dog
cap
cut
elephant

The output file could be:

cat cut cup
cap cat cut cup
cat dog 3 impossible
emu kea impossible
flu covid impossible
car cat impossible