Large Exponents

Let \(x\) be defined as follows: \(x = 1^{2013} + 2^{2013} + 3^{2013} + \ldots + 2014^{2013}\)

And for every \( i \), let \(Z_i\) be the smallest non-negative integer such that: \( x \equiv Z_i \pmod{i} \)

Calculate the value of \( 2 \cdot Z_{2013} + Z_{2014} + 5 \cdot Z_{2015} - 100 \cdot Z_{2016} \)

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