When I hit my pocket...

AtCoder

IDyahoo_procon2019_qual_c

Time2000ms

Memory256MB

Difficulty—

Snuke has one biscuit and zero Japanese yen (the currency) in his pocket. He will perform the following operations exactly $K$ times in total, in the order he likes: * Hit his pocket, which magically increases the number of biscuits by one. * Exchange $A$ biscuits to $1$ yen. * Exchange $1$ yen to $B$ biscuits. Find the maximum possible number of biscuits in Snuke's pocket after $K$ operations. ## Constraints * $1 \leq K,A,B \leq 10^9$ * $K,A$ and $B$ are integers. ## Input Input is given from Standard Input in the following format: $K$ $A$ $B$ [samples]

Samples

Input #1

4 2 6

Output #1

7

The number of biscuits in Snuke's pocket after $K$ operations is maximized as follows:

*   Hit his pocket. Now he has $2$ biscuits and $0$ yen.
*   Exchange $2$ biscuits to $1$ yen. his pocket. Now he has $0$ biscuits and $1$ yen.
*   Hit his pocket. Now he has $1$ biscuits and $1$ yen.
*   Exchange $1$ yen to $6$ biscuits. his pocket. Now he has $7$ biscuits and $0$ yen.

Input #2

7 3 4

Output #2

Input #3

314159265 35897932 384626433

Output #3

48518828981938099

API Response (JSON)

{
  "problem": {
    "name": "When I hit my pocket...",
    "description": {
      "content": "Snuke has one biscuit and zero Japanese yen (the currency) in his pocket. He will perform the following operations exactly $K$ times in total, in the order he likes: *   Hit his pocket, which magical",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "yahoo_procon2019_qual_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Snuke has one biscuit and zero Japanese yen (the currency) in his pocket. He will perform the following operations exactly $K$ times in total, in the order he likes:\n\n*   Hit his pocket, which magical...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments