Consider the following problem, called LONGEST SIMPLE s$$t PATH: Given a directed graph G $=($V$,$ E$,$ w$),$ where w$($e$)$ is defined as a non$-$negative integer for each edge e in E$,$ vertices s$,$ t in V $,$ and a positive integer K$,$ answer YES if there is a simple s $$ t path of total weight at least K$.$ An s $$ t path starts at s and ends at t$,$ a path is simple if it does not repeat any vertices, and the total weight of a path is the sum of the weights of its edges. Prove that the LONGEST SIMPLE s $$ t PATH problem is NP$-$hard. Simplest reduction is from HAMPATH.