Cookies

AtCoder

IDabc440_e

Time2000ms

Memory256MB

Difficulty—

There are $10^{100}$ cookies of each of $N$ types. The deliciousness per cookie of the $i$\-th type is $A_i$. You will choose a total of $K$ cookies from these. Two ways of choosing cookies are considered the same if and only if the multisets of types of chosen cookies match. For each of the $\binom{N+K-1}{K}$ ways of choosing, consider the sum of deliciousness of the chosen cookies. Let $S_1,S_2,\dots$ be these sums in descending order, with duplicates included. Find $S_1,\dots,S_X$. ## Constraints * $1\leq N \leq 50$ * $1 \leq K \leq 10^5$ * $1 \leq X \leq \min\left(10^5, \binom{N+K-1}{K}\right)$ * $-10^9 \leq A_i \leq 10^9$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $K$ $X$ $A_1$ $\dots$ $A_N$ [samples]

Samples

Input #1

2 4 3
20 10

Output #1

80
70
60

There are $5$ ways to choose $4$ cookies: "$k$ cookies of type $1$ and $4-k$ cookies of type $2$" $(0\leq k \leq 4)$, where the sums of deliciousness of the chosen cookies are $80,70,60,50,40$.

Input #2

3 100000 5
-1 -1 -1

Output #2

\-100000
-100000
-100000
-100000
-100000

Different ways of choosing cookies may result in the same sum of deliciousness.

Input #3

9 14142 13
31 41 59 26 53 58 97 93 23

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Cookies",
    "description": {
      "content": "There are $10^{100}$ cookies of each of $N$ types. The deliciousness per cookie of the $i$\\-th type is $A_i$. You will choose a total of $K$ cookies from these. Two ways of choosing cookies are consid",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc440_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $10^{100}$ cookies of each of $N$ types. The deliciousness per cookie of the $i$\\-th type is $A_i$.\nYou will choose a total of $K$ cookies from these. Two ways of choosing cookies are consid...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments