<image>As shown in the figure, triangles \(\triangle OAC\) and \(\triangle BAD\) are both isosceles right triangles, with \(\angle ACO = \angle ADB = 90^{\circ}\). The hyperbola of the inverse proportional function \(y = \dfrac{k}{x}\) passes through point \(B\) in the first quadrant. If \(O{{A}^{2}} - A{{B}^{2}} = 16\), then the value of \(k\) is __________. 
