The number of positive integer pairs \((a,b)\) such that \(a\) divides \(b\) and \(b\) divides \(2013^{2014}\) can be expressed as \(2013n+k\), where \(n\) and \(k\) are integers with \(0 \leq k < 2013\). What is \(k\)? Recall \(2013=3\cdot 11\cdot 61\).

Let's think step by step and output the final answer within \boxed{}.
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