Half and Half

AtCoder

IDarc096_a

Time2000ms

Memory256MB

Difficulty—

"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. Nakahashi 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. ## Constraints * $1 ≤ A, B, C ≤ 5000$ * $1 ≤ X, Y ≤ 10^5$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $A$ $B$ $C$ $X$ $Y$ [samples]

Samples

Input #1

1500 2000 1600 3 2

Output #1

7900

It is optimal to buy four AB-pizzas and rearrange them into two A-pizzas and two B-pizzas, then buy additional one A-pizza.

Input #2

1500 2000 1900 3 2

Output #2

8500

It is optimal to directly buy three A-pizzas and two B-pizzas.

Input #3

1500 2000 500 90000 100000

Output #3

100000000

It 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.

API Response (JSON)

{
  "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 o...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments