Lucky Number

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A positive integer is called "lucky number" if it has exactly \(2014\) positive divisors and can divided by \(2014\). Let \(k\) denote the number of all possibilities of "lucky number" and \(a_{1},a_{2},...,a_{k}\) are all possibilities of "lucky number". If there is a positive integer \(p\) which satisfies \[2014^p|a_{1}a_{2}a_{3}...a_{k}\] ,then determine the maximum value of \(p\) which possible.

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