Consider the following number \( S=\sum _{ n=1 }^{ 37 }{ 9(37^{ n }) } \).

Suppose \(K\) is the number of non-zero elements of row \(S+1\) of Pascal's triangle in modulo \(37\). (To make this clear, row \(S+1\) would be the row with \(S+1\) elements) What is \(\log _{ 10 }{ K } \)?

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