Increasing Minimum

AtCoder

IDarc130_e

Time2000ms

Memory256MB

Difficulty—

Consider doing the operation below on a sequence of $N$ positive integers $A = (A_1, A_2, \ldots, A_N)$ to obtain a sequence $I = (i_1, i_2, \ldots, i_K)$. * For each $k = 1, 2, \ldots, K$ in this order, do the following. * Choose an $i$ such that $A_i = \min{A_1, A_2, \ldots, A_N}$. * Let $i_k = i$. * Add $1$ to $A_i$. You are given integers $N$, $K$, and a sequence $I$. Determine whether there exists a sequence of positive integers $A$ for which it is possible to obtain $I$ from the operation. If it exists, find the lexicographically smallest such sequence. ## Constraints * $1\leq N, K\leq 3\times 10^5$ * $1\leq i_k\leq N$ ## Input Input is given from Standard Input in the following format: $N$ $K$ $i_1$ $i_2$ $\ldots$ $i_K$ [samples]

Samples

Input #1

4 6
1 1 4 4 2 1

Output #1

1 3 3 2

Some of the sequences for which it is possible to obtain $I = (1,1,4,4,2,1)$ from the operation are $(1, 3, 3, 2)$ and $(2, 4, 5, 3)$. The lexicographically smallest among them is $(1, 3, 3, 2)$.

Input #2

4 6
2 2 2 2 2 2

Output #2

6 1 6 6

Input #3

4 6
1 1 2 2 3 3

Output #3

\-1

API Response (JSON)

{
  "problem": {
    "name": "Increasing Minimum",
    "description": {
      "content": "Consider doing the operation below on a sequence of $N$ positive integers $A = (A_1, A_2, \\ldots, A_N)$ to obtain a sequence $I = (i_1, i_2, \\ldots, i_K)$. *   For each $k = 1, 2, \\ldots, K$ in this ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc130_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Consider doing the operation below on a sequence of $N$ positive integers $A = (A_1, A_2, \\ldots, A_N)$ to obtain a sequence $I = (i_1, i_2, \\ldots, i_K)$.\n\n*   For each $k = 1, 2, \\ldots, K$ in this ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments