A Oscillatory integral in light-cone coordinates

I am trying to evaluate an integral in light-cone coordinates
Where light-cone coordinates in 1+1D are defined by
$x^+=frac{x^0+x^1}{sqrt 2}$ and $x^-=frac{x^0-x^1}{sqrt 2}$.

The integral that I need to evaluate is
$$int dk^+dk^-e^{-imath kcdot x}frac{1}{-2k^+k^-},$$ can have any method to do it,
If not can we do the definite integral that $k^+$ and $k^-$ vary from $-infty to infty$