P7713 "EZEC-10" Scoring

**To prevent the judge from being hacked, the time limit for this problem is 100 ms.**

Little A goes to the Olympics. There are $n$ judges in total, who give Little A scores $a_1,a_2,\ldots,a_n$. Little A is not satisfied with his scores, so he increases the score given by one judge by $1$. This is called one operation. However, Little A cannot be too greedy: he can perform at most $m$ operations. Little A's final score is the average of all scores after removing one highest score and one lowest score. Little A wants to know the maximum possible final score.

The first line contains two integers $n,m$. The second line contains $n$ integers $a_1,a_2,\ldots,a_n$.

For easier output, Little A only needs to know what **final score $\times (n-2)$** is.

**[Sample 1 Explanation]** One feasible plan is: $[1,2,3]\to [3,2,3]$. **[Sample 2 Explanation]** One feasible plan is: $[1,2,2,3]\to [2,3,3,3]$. **[Constraints and Notes]** **This problem uses bundled testdata.** - Subtask 1 (5 points): $m=0$. - Subtask 2 (10 points): $n=3$. - Subtask 3 (15 points): $n,m\le 10^3$. - Subtask 4 (70 points): no special restrictions. For $100\%$ of the testdata, $3\le n\le 10^5$, $0\le m,a_i\le 10^9$. Translated by ChatGPT 5