Almost Multiplication Table

AtCoder

IDagc061_d

Time3000ms

Memory256MB

Difficulty—

There are positive integers $N, M$, and an $N \times M$ positive integer matrix $A_{i, j}$. For two **(strictly) increasing** positive integer sequences $X = (X_1, \ldots, X_N)$ and $Y = (Y_1, \ldots, Y_M)$, we define the penalty $D(X, Y)$ as $\max_{1 \leq i \leq N, 1 \leq j \leq M} |X_i Y_j - A_{i, j}|$. Find two **(strictly) increasing** positive integer sequences $X$ and $Y$ such that $D(X, Y)$ is the smallest possible. ## Constraints * $1 \leq N, M \leq 5$ * $1 \leq A_{i, j} \leq 10^9$ ($1 \leq i \leq N$, $1 \leq j \leq M$) * All values in the input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_{1,1}$ $\ldots$ $A_{1,M}$ $\vdots$ $A_{N,1}$ $\ldots$ $A_{N,M}$ [samples]

Samples

Input #1

1 1
853922530

Output #1

0
31415
27182

Input #2

Output #2

5
1 2 3 
1 2 3

Input #3

3 4
4674 7356 86312 100327
8737 11831 145034 167690
47432 66105 809393 936462

Output #3

357
129 216 1208 
39 55 670 775

API Response (JSON)

{
  "problem": {
    "name": "Almost Multiplication Table",
    "description": {
      "content": "There are positive integers $N, M$, and an $N \\times M$ positive integer matrix $A_{i, j}$. For two **(strictly) increasing** positive integer sequences $X = (X_1, \\ldots, X_N)$ and $Y = (Y_1, \\ldots,",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc061_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are positive integers $N, M$, and an $N \\times M$ positive integer matrix $A_{i, j}$. For two **(strictly) increasing** positive integer sequences $X = (X_1, \\ldots, X_N)$ and $Y = (Y_1, \\ldots,...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments