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Algebra Level 3

If the value of

(1+12+13++12014)(12+13+14++12015)\left(1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{2014}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\cdots+\frac{1}{2015}\right) (1+12+13++12015)(12+13+14++12014)-\left(1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{2015}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\cdots+\frac{1}{2014}\right)

is ab\frac{a}{b} for relatively prime aa and bb, then the value of a+ba+b is

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