We have the following two problems:

$-$ Longest$-$Path$-$Length $-$ you are given a undirected graph and two vertices $\backslash ($ s$,$ t $\backslash )$ and returns the number of edges in the longest simple path between the two vertices.

$-$ Longest$-$Path $-$ you are given a graph $\backslash ($ G$=($V$,$ E$)\backslash ),$ two vertices $\backslash ($ u$,$ v $\backslash$in V $\backslash ),$ an integer $\backslash ($ k $\backslash$geq $0\backslash ),$ and the problem outputs whether or not there is a simple path from $\backslash ($ u $\backslash )$ to $\backslash ($ v $\backslash )$ in $\backslash ($ G $\backslash )$ containing atleast $\backslash ($ k $\backslash )$ edges.

Show that the optimization problem, Longest$-$Path$-$Length can be solved in polynomial time if and only if Longest$-$Path $\backslash (\backslash$in P $\backslash )$