$4.$ A and B are married and own an apartment together. A purchased the apartment for $$1,000,000$ and titled it as A and B joint tenants with rights of survivorship. A and B lived in the apartment as their principal residence from $2020$ to $2023.$ A and B moved to Paris in $2024.$ A is a U$.$S$.$ citizen, B is not. A and B sold the apartment in $2025$ for $$5,000,000.$

a$.$ What income gain or loss do A and B recognize in $2025?$