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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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