Let \( P \) be the parabola with equation \( y = x^2 \). There are real numbers \( r \) and \( s \) such that the line with slope \( m \) passing through the point \( Q = (3, 7) \) does not intersect \( P \) if and only if \( r < m < s \). Find \( r + s \). Let's think step by step and output the final answer within \boxed{}.
user