Decimal cryptarithm

Logic Level 4

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

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

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

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