Find the Number of Possible Ways for an Event

Description

You are given three integers n, x, and y.

An event is being held for n performers. When a performer arrives, they are assigned to one of the x stages. All performers assigned to the same stage will perform together as a band, though some stages might remain empty.

After all performances are completed, the jury will award each band a score in the range [1, y].

Return the total number of possible ways the event can take place.

Since the answer may be very large, return it modulo 109 + 7.

Note that two events are considered to have been held differently if either of the following conditions is satisfied:

- Any performer is assigned a different stage.

- Any band is awarded a different score.