$f(x)$ is a polynomial of degree 99. For exactly 100 (out of 101) integer values ranging from $0$ to $100$, we have $f(x) = \frac {1}{x+1}$. Also, $f(101) = 0$. For what value of $a$, $0 \leq a \leq 100$ is $f(a) \neq \frac {1}{a+1}$?

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