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

An event has n performers and x available stages.

The event is organized according to the following conditions:

• Each performer is assigned to exactly one stage.

• Each stage that contains at least one performer forms a band.

• Each band is awarded an integer score between $1$ and y, inclusive.

Return the total number of possible ways to organize the event. Since the answer may be very large, return it modulo $10^9 + 7$.

Constraints:

• $1 \le$ n, x, y $\le 1000$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.