Score : $300$ points

问题描述

在高桥王国中有 $N$ 名公民。每位公民都有一个国家身份证号码；第 $i$ 位公民的身份证号码为 $a_i$。这里，所有的 $a_i$ 都两两不同。

高桥有 $K$ 块糖果。他决定按照以下方式将这些糖果分发给公民，直到糖果分完为止。

• 当他拥有不少于 $N$ 块糖果时，向每一位公民分发一块糖果。
• 否则，设 $K'$ 为他当前拥有的糖果数量，并将一块糖果分发给身份证号码最小的 $K'$ 位公民。

当所有糖果都分发完毕后，第 $i$ 位公民将会获得多少块糖果？

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

There are $N$ citizens in the Kingdom of Takahashi. Each citizen has a national ID number; the ID of the $i$-th citizen is $a_i$. Here, all $a_i$ are pairwise different.

Takahashi has $K$ pieces of sweets. He has decided to hand out these pieces to the citizens in the following way until he has no more pieces.

• When he has $N$ or more pieces, hand out one piece to every citizen.
• Otherwise, let $K'$ be the number of pieces he has at the moment, and hand out one piece to each of the citizens with the $K'$ smallest IDs.

When all pieces are handed out, how many pieces will the $i$-th citizen have?

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq K \leq 10^{18}$
• $1 \leq a_i \leq 10^9$
• All $a_i$ are pairwise different.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $K$

$a_1$ $a_2$ $\ldots$ $a_N$

Output

Print $N$ lines. The $i$-th line should contain the number of pieces of sweets received by the $i$-th citizen.

Sample Input 1

2 7
1 8

Sample Output 1

4
3

Takahashi will hand out the pieces as follows.

• Hand out one piece to everyone, leaving Takhashi with $5$ pieces.
• Hand out one piece to everyone, leaving Takhashi with $3$ pieces.
• Hand out one piece to everyone, leaving Takhashi with $1$ piece.
• Hand out one piece to the $1$-st citizen, leaving Takhashi with no pieces.

In the end, the $1$-st citizen will receive $4$ pieces, and the $2$-nd citizen will receive $3$ pieces.

Sample Input 2

1 3
33

Sample Output 2

3

Since there is just one citizen, Takahashi will hand out all pieces to that $1$-st citizen.

Sample Input 3

7 1000000000000
99 8 2 4 43 5 3

Sample Output 3

142857142857
142857142857
142857142858
142857142857
142857142857
142857142857
142857142857

update @ 2024/3/10 09:21:45