We have a $K$-connected graph. This graph has non empty disjoint subsets $S_1$ and $S_2$ of $V(G)$. How to show that there exist $k$ internally disjoint paths $P_1, P_2, \ldots, P_K$ such that each path $P_i$ is a $u-v$ path for some $u \in S_1$ and some $v \in S_2$ for $i = 1,2,\ldots,k$ and $|S_1 \cap V(P_i)| = |S_2 \cap V(P_i)| = 1$.
I know there exists $k$ internal paths but how to prove that these paths are disjoint? Any help would be appreciated.