Inverse Fourier transform of (s ↦ e^{-s})

[serene spindle]

It doesn't exist as a function since the integral is divergent, but can it be realized as a generalized function (or distribution)?
For example, the constant function (s ↦ 1) has inverse Fourier transform being the Dirac's delta which is a distribution.

[serene spindle]

nevermind, just realized that wasn't the question i should be thinking of lmao