{"problem":{"name":"Half and Half","description":{"content":"\"Pizza At\", a fast food chain, offers three kinds of pizza: \"A-pizza\", \"B-pizza\" and \"AB-pizza\". A-pizza and B-pizza are completely different pizzas, and AB-pizza is one half of A-pizza and one half o","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc096_a"},"statements":[{"statement_type":"Markdown","content":"\"Pizza At\", a fast food chain, offers three kinds of pizza: \"A-pizza\", \"B-pizza\" and \"AB-pizza\". A-pizza and B-pizza are completely different pizzas, and AB-pizza is one half of A-pizza and one half of B-pizza combined together. The prices of one A-pizza, B-pizza and AB-pizza are $A$ yen, $B$ yen and $C$ yen (yen is the currency of Japan), respectively.\nNakahashi needs to prepare $X$ A-pizzas and $Y$ B-pizzas for a party tonight. He can only obtain these pizzas by directly buying A-pizzas and B-pizzas, or buying two AB-pizzas and then rearrange them into one A-pizza and one B-pizza. At least how much money does he need for this? It is fine to have more pizzas than necessary by rearranging pizzas.\n\n## Constraints\n\n*   $1 ≤ A, B, C ≤ 5000$\n*   $1 ≤ X, Y ≤ 10^5$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$A$ $B$ $C$ $X$ $Y$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc096_a","tags":[],"sample_group":[["1500 2000 1600 3 2","7900\n\nIt is optimal to buy four AB-pizzas and rearrange them into two A-pizzas and two B-pizzas, then buy additional one A-pizza."],["1500 2000 1900 3 2","8500\n\nIt is optimal to directly buy three A-pizzas and two B-pizzas."],["1500 2000 500 90000 100000","100000000\n\nIt is optimal to buy $200000$ AB-pizzas and rearrange them into $100000$ A-pizzas and $100000$ B-pizzas. We will have $10000$ more A-pizzas than necessary, but that is fine."]],"created_at":"2026-03-03 11:01:14"}}