Min Manhattan Distance

You are given two sets of points $S$ and $T$ on the $xy$-plane. $S$ contains $N$ points and $T$ contains $M$ points. The points $(x_i, y_i)$ in $T$ have a special property - for every $1\leq i \lt M$, $x_{i+1} \gt x_i$ and $y_{i+1} \lt y_i$. For each point $(x, y) \in T$, find the minimum [Manhattan distance](https://en.wikipedia.org/wiki/Taxicab_geometry#Formal_definition) between $(x, y)$ and