# Decimal cryptarithm

Logic Level 4

$\overline{EVE} \div \overline{DID} = 0. \overline{TALKTALKTALKTALK\ldots}$

Given that $$E,V,D,I,T,A,L$$ and $$K$$ are distinct single digits and let $$\overline{EVE}$$ and $$\overline{DID}$$ be two coprime 3-digit positive integers and $$\overline{TALK}$$ be a 4-digit integer, such that the equation above holds true, where the right hand side of the equation is a repeating decimal number.

Find the value of the sum $$\overline{EVE} + \overline{DID} + \overline{TALK}$$.

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