Define a sequence recursively by $x_0=3$ and

$x_{n+1}=\frac{x_n^2+3x_n+2}{x_n+4}$

for all nonnegative integers $n$. Let $m$ be the least positive integer such that

$x_m\le 2+\frac{1}{5^{10}}$.

In which of the following intervals does $m$ lie?