If the line \( x - 2y = m \, (m \in \mathbb{Z}) \) intersects the circle \( x^{2} + y^{2} = 2x + 4y \) at two distinct points, then the number of possible values of \( m \) are
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Geometry Tip:
If $d<r$, the line is a secant (intersects at 2 points).
If $d = r$, the line is a tangent (touches at 1 point).
If $d>r$, the line does not intersect the circle.