$(15$ points$)$ Let $T$ and $U$ be $(2,4)$ trees storing $n$ and $m$ entries, respectively, such that all

the entries in $T$ have keys less than the keys of all the entries in $U.$ Describe an

$O(logn+logm)$ time method for joining $T$ and $U$ into a single $2-4$ tree that stores all the

entries in $T$ and $U.$ Assume that $T$ and U have heights $h_t$ and $h_u$ and $h_t>h_u.$