How can I add product_type (simple, variable etc) select dropdown on a jetengine form to add woocommerce products on the front end?

Question

I have been trying for a while but I cant get this right. I am trying to add a jetengine form but can add all the other fields except the product_type because it needs to be variable as selected but by default it selects simple which is fine becuase other products I want to add are simple but this one is a variable. Please can you assit me?

I have tried product_type, _type but not one saves the terms, When I log into the backend it shows as simple product created.