A cohort of K spies resident in a certain country needs escape routes in case of emergency. They

will be traveling using the railway system which we can think of as a directed graph G $=($V$,$ E$),$

with V being the cities and E being the $($directed$)$ railway roads between cities. Each spy i has a

starting city si in V$,$ different from the other spies$$ starting cities and needs to reach a consulate

city of any friendly nation; these consulate cities are a known set of cities $\{$t$1,...,$ tl $\}$ V of

cardinality l$.$ In order to move undetected, the spies agree that at most C of them should ever pass

through any one city of V$.$ We are interested in designing an efficient algorithm that computes

paths for each of the spies $($or detects that the requirements cannot be met$).$

a $(1$ point$)$ Explain how to modify the graph appropriately to create a max$-$flow instance.

b $(0\mathrm{.}5$ points$)$ What algorithm should you run in the modified graph? What is the running

time of your algorithm in terms of V$,$ E$?$