Constrained Nim 2

AtCoder

IDabc297_g

Time2000ms

Memory256MB

Difficulty—

There are $N$ piles of stones. Initially, the $i$\-th pile contains $A_i$ stones. With these piles, Taro the First and Jiro the Second play a game against each other. Taro the First and Jiro the Second make the following move alternately, with Taro the First going first: * Choose a pile of stones, and remove between $L$ and $R$ stones (inclusive) from it. A player who is unable to make a move loses, and the other player wins. Who wins if they optimally play to win? ## Constraints * $1\leq N \leq 2\times 10^5$ * $1\leq L \leq R \leq 10^9$ * $1\leq A_i \leq 10^9$ * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $L$ $R$ $A_1$ $A_2$ $\ldots$ $A_N$ [samples]

Samples

Input #1

3 1 2
2 3 3

Output #1

First

Taro the First can always win by removing two stones from the first pile in his first move.

Input #2

5 1 1
3 1 4 1 5

Output #2

Second

Input #3

7 3 14
10 20 30 40 50 60 70

Output #3

First

API Response (JSON)

{
  "problem": {
    "name": "Constrained Nim 2",
    "description": {
      "content": "There are $N$ piles of stones. Initially, the $i$\\-th pile contains $A_i$ stones. With these piles, Taro the First and Jiro the Second play a game against each other. Taro the First and Jiro the Secon",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc297_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ piles of stones. Initially, the $i$\\-th pile contains $A_i$ stones. With these piles, Taro the First and Jiro the Second play a game against each other.\nTaro the First and Jiro the Secon...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments