Absolute solution

\[|x^2-xy-y^2|=1\] The solutions for the equation above are \((x_1,y_1), (x_2,y_2), (x_3,y_3),\dots\), where \(x\) and \(y\) are two natural numbers.

Which is bigger, \(A\) or \(B\)? \[\begin{align} A & = x_1^2+x_2^2+x_3^2+x_4^2+\dots+x_{2017}^2 \\ \ \\ B & = y_{2018}\times y_{2019}\end{align}\]

Note: For any positive integer \(k\), \(x_k\leq x_{k+1}\).

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