Let $P$ be a monic polynomial of degree 2017 such that $P(1) = P(2) = \cdots = P(2016) = 0$ and $P(0) = 2018!$ .

Find the largest root of $P(x)$ .

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

The answer is 2016.

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Since $P(1)= P(2) = P(3) = ... = P(2016) =0$ , we can see that ${1,2,3,...,2016}$ are the roots of $P(x)$ . Then, the largest root of $P(x)$ is $2016$ .