2026 Fermat Problem 23

The string of digits 123451234551234555\ldots is formed by alternately writing the digits 1234, in that order, and then writing some number of consecutive 5s. There are exactly k consecutive 5s immediately following the kth occurrence of 1234. If S is the sum of the first 2026 digits of the string, what is the sum of the digits of S?

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