A circle of radius $2$ has center at $(2,0)$. A circle of radius $1$ has center at $(5,0)$.  A line is tangent to the two circles at points in the first quadrant.  What is the $y$-intercept of the line?The answer is in the form k\sqrt{m}+n,. Please provide the value of k + m + n.

Let's think step by step and output the final answer within \boxed{}.
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