Let \(x\) be a real number and \(f(x)\) be a real-valued function on \(x\) such that \(f(x)\) is:

the next palindrome larger than \(x\) (if \(x\) is not a palindrome); or

\(x\) (if \(x\) is a palindrome).

For example, \(f(1001)=1001\),\(f(1001.01)=f(1002)=1111\).

Let

\[A=\int _{ 999 }^{ 2015 }{ f(x) \mbox{ } dx } \]

\[B=f(...(f(f(1603)-58)-58)...)-58\]

Find the value of \(\frac{A}{B}\).

*This problem is part of the set 2015 Countdown Problems.*

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