Which distribution x should follow to get the results, xy follows normal distribution, if y is standard normal random variable?

Question

I have two independent random variables $x$ and $y$.

Let's assume that y follows a standard normal distribution, $N(0,1)$

I want some results that $xy\~N(a,b)$ (e.g. $a=0$ and $b=1$)

Which distribution $x$ should follow to get Gaussian distribution random variable, $xy$?