Vector Calculus · Hard problem

The field $\mathbf F = (2xy + az,\; x^2 + bz,\; 3x + 2y)$ is conservative on all of space for exactly one pair of constants $a, b$. For that pair, find the work done by $\mathbf F$ along any path from $(0, 0, 0)$ to $(1, 2, 3)$.