R sample from mixture distribution

How could I sample from this distribution:

given: 𝑝(𝑦) = 𝑃(𝑌 = 𝑦|𝑌~𝑃(𝜆/2)) , where 𝑃(𝜆/2) is the Poisson distribution with lamda/2 and

𝑔(𝑥|𝑦) follows the chi square distribution with df=n+2y

Many thanks!!