Mex of Subset Sum

AtCoder

IDagc062_c

Time2000ms

Memory256MB

Difficulty—

You are given an integer sequence of length $N$: $A=(A_1,A_2,\dots,A_N)$. Find the $K$ smallest positive integers $X$ that satisfy the following condition. * There is **no** non-empty (not necessarily contiguous) subsequence of $A$ whose elements sum to $X$. ## Constraints * $1 \leq N \leq 60$ * $1 \leq K \leq 1000$ * $1 \leq A_i \leq 10^{15}$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $K$ $A_1$ $A_2$ $\dots$ $A_N$ [samples]

Samples

Input #1

3 3
1 2 5

Output #1

4 9 10

The subsequences of $A$ are $(1),(2),(1,2),(5),(1,5),(2,5),(1,2,5)$, and their respective sums are $1,2,3,5,6,7,8$. Therefore, for $X=1,2,3,5,6,7,8$, there are subsequences of $A$ whose elements sum to $X$.
On the other hand, for $X=4,9,10$, there is no subsequence of $A$ whose elements sum to $X$.

Input #2

20 10
324 60 1 15 60 15 1 60 319 1 327 1 2 60 2 345 1 2 2 15

Output #2

14 29 44 59 74 89 104 119 134 149

API Response (JSON)

{
  "problem": {
    "name": "Mex of Subset Sum",
    "description": {
      "content": "You are given an integer sequence of length $N$: $A=(A_1,A_2,\\dots,A_N)$. Find the $K$ smallest positive integers $X$ that satisfy the following condition. *   There is **no** non-empty (not necessar",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc062_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an integer sequence of length $N$: $A=(A_1,A_2,\\dots,A_N)$.\nFind the $K$ smallest positive integers $X$ that satisfy the following condition.\n\n*   There is **no** non-empty (not necessar...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments