A number theory problem by Achal Jain

\[\large x@y = x (x+1)(x+2) \cdots (x+y - 1) \]

The operator \(@\) is defined for positive integers \(x\) and \(y\) as above. Let \(h\) denote the greatest common divisor of \( x @y \) and \(y!\). Which of the following options must be true?

\[\]

Notation: \(!\) is the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).

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