Subset Sum Game

AtCoder

IDagc056_d

Time2000ms

Memory256MB

Difficulty—

There are $N$ integers written on a blackboard. The $i$\-th integer is $A_i$. Here, $N$ is even. Additionally, integers $L$ and $R$ are given. Alice and Bob will play a game. They alternately take turns, with Alice going first. In each turn, the player chooses a number written on the blackboard and erases it. The game will end in $N$ turns. Then, let $s$ be the sum of the integers erased by Alice. If $L \leq s \leq R$, Alice wins; otherwise, Bob wins. Find which player will win when both players play optimally. ## Constraints * $2 \leq N \leq 5000$ * $N$ is even. * $1 \leq A_i \leq 10^9$ * $0 \leq L \leq R \leq \sum_{1 \leq i \leq N} A_i$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $L$ $R$ $A_1$ $A_2$ $\cdots$ $A_N$ [samples]

Samples

Input #1

4 5 6
3 1 4 5

Output #1

Alice

In this game, Alice will always win. Below is a possible progression of the game.

*   Alice erases $1$.
*   Bob erases $4$.
*   Alice erases $5$.
*   Bob erases $3$.

Here, the sum of the integers erased by Alice is $6$. Since $L \leq 6 \leq R$, Alice wins.

Input #2

2 2 3
4 1

Output #2

Bob

Input #3

30 655 688
42 95 9 13 91 27 99 56 64 15 3 11 5 16 85 3 62 100 64 79 1 70 8 69 70 28 78 4 33 12

Output #3

Bob

Input #4

30 792 826
81 60 86 57 5 20 26 13 39 64 89 58 43 98 50 79 58 21 27 68 46 47 45 85 88 5 82 90 74 57

Output #4

Alice

API Response (JSON)

{
  "problem": {
    "name": "Subset Sum Game",
    "description": {
      "content": "There are $N$ integers written on a blackboard. The $i$\\-th integer is $A_i$. Here, $N$ is even. Additionally, integers $L$ and $R$ are given. Alice and Bob will play a game. They alternately take tur",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc056_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ integers written on a blackboard. The $i$\\-th integer is $A_i$. Here, $N$ is even. Additionally, integers $L$ and $R$ are given.\nAlice and Bob will play a game. They alternately take tur...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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