A non-uniform magnetic  field  exists in  the free space  and  given  as  $\overrightarrow{B}=\frac{B_0}{{\ell }^2}{x}^2\widehat{k}$, where   $B_0$  and  $\ell$   are  positive constants.  A  particle  having  positive  charge  ‘q’  and  mass  ‘m’  is  projected  with  speed  ‘ $v_0$’  along positive x-axis from the origin. The maximum distance of the charged particle from the y- axis  before  it  turns  back  due  to  the  magnetic  field is D.  (Ignore  any  interaction  other  than  magnetic field). If  $D={\left(\frac{\alpha m{\ell }^2{v}_0}{q{B}_0}\right)}^{1/\beta }$, where  $\alpha ,\beta$ are positive integers then find the value of  $\alpha times\beta$ ?