A "New" Operation

Algebra Level 3

To every pair of positive real numbers \(x\) and \(y\), we assign a positive real number \(x\star y\) satisfying the two properties that \(x\star x=1\) and \(x\star (y\star z)=(x\star y) \times z\) (where \( \times \) represents standard multiplication). Find \(k\) if \(61\star 2013=\frac{1}{k}\).

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