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Algebra Level 5

Let $P(x)$ be a polynomial of degree 99 satisfying $P(n)=n \cdot 99!$ for $n= 1,2,3,\ldots,99$ . If $P(100)=0$ , find the value of the coefficient of $x^{98}$ in $P(x)$ .

Notation: $!$ denotes the factorial notation. For example, $8! = 1\times2\times3\times\cdots\times8$ .