Don't shoot the animal, hunter!

Probability Level 5

A sportsman's chance of shooting an animal at a distance R(>A)R(>A) is A2R2.\frac{A^{2}}{R^{2}}. He fires when R=2AR=2A and if he misses, he reloads and fires when R=3A,4A,5AR=3A,4A,5A\cdots and so on. If he misses at distance 1729A,1729A, the animals escapes.

If the probability that the animal escapes is ab\frac{a}{b} where aa and bb are coprime integers, what is the value of ba?b-a?

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