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.
\n\nSince 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:
\n\n\n
Example 1:
\n\nInput: n = 1, x = 2, y = 3
\n\nOutput: 6
\n\nExplanation:
\n\nExample 2:
\n\nInput: n = 5, x = 2, y = 1
\n\nOutput: 32
\n\nExplanation:
\n\nExample 3:
\n\nInput: n = 3, x = 3, y = 4
\n\nOutput: 684
\n\n
Constraints:
\n\n1 <= n, x, y <= 1000Compiled with clang 17 using the latest C++ 23 standard, and libstdc++ provided by GCC 13.
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