# Triangles within triangles

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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