Let $L=\{(y_1,...,y_n,S,p)\ |\ \exists I\subset[n]\ s.t. \ |I|=p.\ \sum_{i\in I}y_i=S\}$.
and $\forall\ 1\leq i\leq n\ :y_i \text{ is a positive integer}$,
Assuming $\mathcal{P}\neq\mathcal{NP}$.
Determine whether the following language is in $\mathcal{P}$ or not.