# Did you learn how to subtract?

Level pending

The decimal parts of two irrational numbers in $$(0,1)$$ taken at random are found to $$2014$$ places. The probability that the smaller one can be subtracted from the other without borrowing can be expressed as $$p^k$$, where $$p$$ is a rational number and $$k > 1000$$ is a positive integer. Find the last three digits of $$\lfloor 100(p+k+1) \rfloor$$.

Assume for this question that the digit in first decimal place of the larger number is greater than the digit in that of the other. (As a follow up, can you say what would the probability be, without this assumption?)

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