<image>To boost tourism, a scenic area in our city employs a flexible ticket pricing strategy to attract visitors$$.$$ The ticket price is set at 50 yuan per person. On non-holidays, tickets are sold at a discount of $$a$$ percent, and on holidays, team pricing is used based on the number of people in a team. Specifically, teams with up to $$m$$ people (including $$m$$ people) pay the standard rate$$.$$ For teams with more than $$m$$ people, the first $$m$$ people pay the standard rate, while the rest receive a $$b$$ percent discount$$.$$ Let the number of people in a tourist group be $$x$$, the ticket cost on non-holidays be denoted as $$y_{1}$$ (in yuan), and the ticket cost on holidays be denoted as $$y_{2}$$ (in yuan). The function graphs of $$y_{1}$$ and $$y_{2}$$ versus $$x$$ are shown in the diagram.
$$(1)$$ From the graph, we can observe: $$a=$$ ______ ;_$$b=$$ ______ ;_$$m=$$ ______ ;
$$(2)$$ Directly write the functional relationships between $$y_{1}$$, $$y_{2}$$, and $$x$$;
$$(3)$$ Tour guide Wang Na from a travel agency takes group $$A$$ to the scenic area on May $$1$$, and group $$B$$ to the scenic area on May $$20$$ (a non-holiday), spending a total of 1900 yuan on tickets. The total number of people in $$A$$ and $$B$$ groups combined is 50. Determine the number of people in each of groups $$A$$ and $$B$$.