Aero Mongolia serves both IKT-ULN and ULN-ULG. However, I have no idea where to purchase the tickets and I think the price will be at least twice your budget.
You can get to ULG overland from the Altai region, however it will be 12+ hours from the nearest airport (RGK) and, what's worse, I don't see any reasonable IKT-RGK tickets.