$[....$ For each of the following problems, describe a polynomial$-$time algorithm$/$reduc$-$

tion which solves the problem. You may freely reference reductions and algorithms we have

studied in class $($you can assume you can solve Max Flow in polynomial time, for instance$).$

Provide a reasonable level of justification for your answers.

$($a$)[5$ points$]$ Given a flow network with integer capacities and an integer $T,$ compute an

$s-t$ cut with capacity exactly $T($if possible$).$

$($b$)$ points