102082: [AtCoder]ABC208 C - Fair Candy Distribution

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