Cathy the Cat lives on a coordinate plane and is currently at $(0,0)$ facing west (that is, in the negative $x$-direction). Cathy moves $1$ unit and then turns $90^{\circ }$ right. From there, Cathy moves $2$ units (north) and then turns $90^{\circ }$ right. She then moves $3$ units (east) and again turns $90^{\circ }$ right. Cathy continues her progress, increasing her distance each time by $1$ unit and always turning right. What is the location of the point which Cathy makes the $1000$ right turn?