Stones

AtCoder

IDdp_k

Time2000ms

Memory256MB

Difficulty—

There is a set $A = { a_1, a_2, \ldots, a_N }$ consisting of $N$ positive integers. Taro and Jiro will play the following game against each other. Initially, we have a pile consisting of $K$ stones. The two players perform the following operation alternately, starting from Taro: * Choose an element $x$ in $A$, and remove exactly $x$ stones from the pile. A player loses when he becomes unable to play. Assuming that both players play optimally, determine the winner. ## Constraints * All values in input are integers. * $1 \leq N \leq 100$ * $1 \leq K \leq 10^5$ * $1 \leq a_1 < a_2 < \cdots < a_N \leq K$ ## Input Input is given from Standard Input in the following format: $N$ $K$ $a_1$ $a_2$ $\ldots$ $a_N$ [samples]

Samples

Input #1

2 4
2 3

Output #1

First

If Taro removes three stones, Jiro cannot make a move. Thus, Taro wins.

Input #2

2 5
2 3

Output #2

Second

Whatever Taro does in his operation, Jiro wins, as follows:

*   If Taro removes two stones, Jiro can remove three stones to make Taro unable to make a move.
*   If Taro removes three stones, Jiro can remove two stones to make Taro unable to make a move.

Input #3

2 7
2 3

Output #3

First

Taro should remove two stones. Then, whatever Jiro does in his operation, Taro wins, as follows:

*   If Jiro removes two stones, Taro can remove three stones to make Jiro unable to make a move.
*   If Jiro removes three stones, Taro can remove two stones to make Jiro unable to make a move.

Input #4

3 20
1 2 3

Output #4

Second

Input #5

3 21
1 2 3

Output #5

First

Input #6

1 100000
1

Output #6

Second

API Response (JSON)

{
  "problem": {
    "name": "Stones",
    "description": {
      "content": "There is a set $A = { a_1, a_2, \\ldots, a_N }$ consisting of $N$ positive integers. Taro and Jiro will play the following game against each other. Initially, we have a pile consisting of $K$ stones. T",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "dp_k"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a set $A = { a_1, a_2, \\ldots, a_N }$ consisting of $N$ positive integers. Taro and Jiro will play the following game against each other.\nInitially, we have a pile consisting of $K$ stones. T...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments