Missing pair

Let $$n=1000000$$, $$s'$$ be the sum of the numbers in input, $$s = \sum_{k=1}^n - s' = \frac{n*(n+1)}{2} - s'$$1, $$q'$$ be the sum of the squares of the numbers in input, $$q = \sum_{k=1}^n k^2 - q' = \frac{2*n^3+3*n^2+n}{6} - q'$$2

Now let $$x+y = s$$ and $$x^2+y^2=q$$ if we put these two equations in a system and solve it we get $$x = \frac{s + \sqrt[2]{2*q-s^2}}{2}$$ and $$y = \frac{s - \sqrt[2]{2*q-s^2}}{2}$$.

Sample inputs:

• Input 1: $$x = 950956$$, $$y = 55729$$
• Input 2: $$x = 149571$$, $$y = 52368$$