+/- Rectangle

AtCoder

IDagc016_c

Time2000ms

Memory256MB

Difficulty—

You are given four integers: $H$, $W$, $h$ and $w$ ($1 ≤ h ≤ H$, $1 ≤ w ≤ W$). Determine whether there exists a matrix such that all of the following conditions are held, and construct one such matrix if the answer is positive: * The matrix has $H$ rows and $W$ columns. * Each element of the matrix is an integer between $-10^9$ and $10^9$ (inclusive). * The sum of all the elements of the matrix is positive. * The sum of all the elements within every subrectangle with $h$ rows and $w$ columns in the matrix is negative. ## Constraints * $1 ≤ h ≤ H ≤ 500$ * $1 ≤ w ≤ W ≤ 500$ ## Input Input is given from Standard Input in the following format: $H$ $W$ $h$ $w$ [samples]

Samples

Input #1

3 3 2 2

Output #1

Yes
1 1 1
1 -4 1
1 1 1

The sum of all the elements of this matrix is $4$, which is positive. Also, in this matrix, there are four subrectangles with $2$ rows and $2$ columns as shown below. For each of them, the sum of all the elements inside is $-1$, which is negative.

![image](https://atcoder.jp/img/agc016/bbdb651fa1f05996886da9f0c4d8090a.png)

Input #2

2 4 1 2

Output #2

No

Input #3

3 4 2 3

Output #3

Yes
2 -5 8 7
3 -5 -4 -5
2 1 -1 7

API Response (JSON)

{
  "problem": {
    "name": "+/- Rectangle",
    "description": {
      "content": "You are given four integers: $H$, $W$, $h$ and $w$ ($1 ≤ h ≤ H$, $1 ≤ w ≤ W$). Determine whether there exists a matrix such that all of the following conditions are held, and construct one such matrix",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc016_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given four integers: $H$, $W$, $h$ and $w$ ($1 ≤ h ≤ H$, $1 ≤ w ≤ W$). Determine whether there exists a matrix such that all of the following conditions are held, and construct one such matrix...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments