Given nonnegative integers $m$ and $n,$ an $(m,n)-$lattice path is a sequence of steps of

distance $1$ either in the $+x$ direction or the $+y$ direction that starts at the origin $(0,0)$

and ends at the point $(m,n).$ For example, here are all $10(3,2)-$lattice paths.

$($a$)$ Describe a bijection between the set of $(m,n)-$lattice paths and the set of binary

words of length $m+n$ with $m1\text{'}$s and $n0\text{'}$s$.$