\(n!\) or \(n\)-factorial is the product of all integers from \(1\) up to \(n\) \((n! = 1 \times 2 \times 3 \times ... \times n)\). Let's denote \(n!!\) be the product of all factorials from \(1!\) up to \(n!\) \((n!! = 1! \times 2! \times 3! \times ... \times n!)\). Let's also denote \(n!!!\) be the product of all double factorials from \(1!!\) up to \(n!!\) \((n!!! = 1!! \times 2!! \times 3!! \times ... \times n!!)\). Find the maximum integral value of \(k\) such that \(2014^k\) divides \(2014!!!\)

You may also try these problems:

Divisible by this year??? (Part 2: Factorials)

Divisible by this year??? (Part 3: What if I did this?)

**This problem is part of the set "Symphony"**

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