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

n!n! or nn-factorial is the product of all integers from 11 up to nn (n!=1×2×3×...×n)(n! = 1 \times 2 \times 3 \times ... \times n). Let's denote n!!n!! be the product of all factorials from 1!1! up to n!n! (n!!=1!×2!×3!×...×n!)(n!! = 1! \times 2! \times 3! \times ... \times n!). Find the maximum integral value of kk such that 2014k2014^k divides 2014!!2014!!

You may also try these problem:

Divisible by this year???

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

This problem is part of the set "Symphony"


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