3317 - Find the Number of Possible Ways for an Event.

Hard

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 <code>10⁹ + 7</code>.

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.

Example 1:

Input: n = 1, x = 2, y = 3

Output: 6

Explanation:

• There are 2 ways to assign a stage to the performer.

• The jury can award a score of either 1, 2, or 3 to the only band.

Example 2:

Input: n = 5, x = 2, y = 1

Output: 32

Explanation:

• Each performer will be assigned either stage 1 or stage 2.

• All bands will be awarded a score of 1.

Example 3:

Input: n = 3, x = 3, y = 4

Output: 684

Constraints:

• 1 <= n, x, y <= 1000