Cutoff

AtCoder

IDabc321_b

Time2000ms

Memory256MB

Difficulty—

There is an exam structured as follows. * The exam consists of $N$ rounds called round $1$ to $N$. * In each round, you are given an integer score between $0$ and $100$, inclusive. * Your final grade is the sum of the $N-2$ of the scores earned in the rounds excluding the highest and lowest. * Formally, let $S=(S_1,S_2,\dots,S_N)$ be the sequence of the scores earned in the rounds sorted in ascending order, then the final grade is $S_2+S_3+\dots+S_{N-1}$. Now, $N-1$ rounds of the exam have ended, and your score in round $i$ was $A_i$. Print the minimum score you must earn in round $N$ for a final grade of $X$ or higher. If your final grade will never be $X$ or higher no matter what score you earn in round $N$, print `-1` instead. Note that your score in round $N$ can only be an integer between $0$ and $100$. ## Constraints * All input values are integers. * $3 \le N \le 100$ * $0 \le X \le 100 \times (N-2)$ * $0 \le A_i \le 100$ ## Input The input is given from Standard Input in the following format: $N$ $X$ $A_1$ $A_2$ $\dots$ $A_{N-1}$ [samples]

Samples

Input #1

5 180
40 60 80 50

Output #1

70

Your scores in the first four rounds were $40$, $60$, $80$, and $50$.  
If you earn a score of $70$ in round $5$, the sequence of the scores sorted in ascending order will be $S=(40,50,60,70,80)$, for a final grade of $50+60+70=180$.  
It can be shown that $70$ is the minimum score you must earn for a final grade of $180$ or higher.

Input #2

3 100
100 100

Output #2

0

Your scores in the first two rounds were $100$ and $100$.  
If you earn a score of $0$ in round $3$, the sequence of the scores sorted in ascending order will be $S=(0,100,100)$, for a final grade of $100$.  
Note that the highest score, $100$, is earned multiple times, and only one of them is excluded. (The same goes for the lowest score.)  
It can be shown that $0$ is the minimum score you must earn for a final grade of $100$ or higher.

Input #3

5 200
0 0 99 99

Output #3

\-1

Your scores in the first four rounds were $0$, $0$, $99$, and $99$.  
It can be shown that your final grade will never be $200$ or higher no matter what score you earn in round $5$.

Input #4

10 480
59 98 88 54 70 24 8 94 46

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Cutoff",
    "description": {
      "content": "There is an exam structured as follows. *   The exam consists of $N$ rounds called round $1$ to $N$. *   In each round, you are given an integer score between $0$ and $100$, inclusive. *   Your final",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc321_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is an exam structured as follows.\n\n*   The exam consists of $N$ rounds called round $1$ to $N$.\n*   In each round, you are given an integer score between $0$ and $100$, inclusive.\n*   Your final...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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