Suppose that $a$ is an integer. A sequence $x_{1}, x_{2}, x_{3}, x_{4}, \ldots$ is constructed with

- $x_{1}=a$,
- $x_{2 k}=2 x_{2 k-1}$ for every integer $k \geq 1$, and
- $x_{2 k+1}=x_{2 k}-1$ for every integer $k \geq 1$.

For example, if $a=2$, then

$$
x_{1}=2 \quad x_{2}=2 x_{1}=4 \quad x_{3}=x_{2}-1=3 \quad x_{4}=2 x_{3}=6 \quad x_{5}=x_{4}-1=5
$$

and so on. The integer $N=578$ can appear in this sequence after the 10th term (for example, $x_{12}=578$ when $a=10$ ), but the integer 579 does not appear in the sequence after the 10th term for any value of $a$. What is the smallest integer $N>1395$ that could appear in the sequence after the 10th term for some value of $a$ ?