Fair Candy Distribution

AtCoder

IDabc208_c

Time2000ms

Memory256MB

Difficulty—

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: $N$ $K$ $a_1$ $a_2$ $\ldots$ $a_N$ [samples]

Samples

Input #1

2 7
1 8

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.

Input #2

1 3
33

Output #2

3

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

Input #3

7 1000000000000
99 8 2 4 43 5 3

Output #3

142857142857
142857142857
142857142858
142857142857
142857142857
142857142857
142857142857

API Response (JSON)

{
  "problem": {
    "name": "Fair Candy Distribution",
    "description": {
      "content": "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 s",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc208_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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.\nTakahashi has $K$ pieces of s...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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