问题 B: Make the Farm great again

Bessie, the chairman of the United Farm of Amoorica, will ends its term in January. An election is being held with N candidates numbered 1,2,…,$N$. 

There are K votes, some of which have been counted so far. Up until now, candidate $i$ has received $A_i$ votes.

After all ballots are counted, candidate i ($1 \le i \le N $) will be elected if and only if the number of candidates who have received more votes than them is less than $M$. There may be multiple candidates elected

For each candidate, find the minimum number of additional votes they need from the remaining ballots to guarantee their victory regardless of how the other candidates receive votes.

Formally, solve the following problem for each $\mathrm{<span\; style="font-family:Arial;">i</span>}<span\; style="font-family:Arial;">=</span>\mathrm{<span\; style="font-family:Arial;">1</span>}<span\; style="font-family:Arial;">,</span>\mathrm{<span\; style="font-family:Arial;">2</span>}<span\; style="font-family:Arial;">,</span><span\; style="font-family:Arial;">\dots </span><span\; style="font-family:Arial;">,</span>\mathrm{<span\; style="font-family:Arial;">N</span>}$.

Determine if there is a non-negative integer $X$ not exceeding $K-\sum_{i=1}^N A_i$ satisfying the following condition. If it exists, find the minimum possible such integer.

• If candidate $\mathrm{<span\; style="font-family:Arial;">i</span>}$ receives $\mathrm{<span\; style="font-family:Arial;">X</span>}$ additional votes, then candidate $\mathrm{<span\; style="font-family:Arial;">i</span>}$ will always be elected.

注意：输出的最后不要带空格。

The input is given from Standard Input in the following format:

$N \qquad M \qquad K$

$A_1 \qquad A_2 \qquad ... \qquad A_N$

If candidate $i$ has already secured their victory, then let $C_i = 0$ . If candidate $i$ cannot secure their victory under any circumstances, then let $C_i = -1$.

5 2 16
3 1 4 1 5

2 -1 1 -1 0