fLIP

AtCoder

IDcode_festival_2017_quala_b

Time2000ms

Memory256MB

Difficulty—

We have a grid with $N$ rows and $M$ columns of squares. Initially, all the squares are white. There is a button attached to each row and each column. When a button attached to a row is pressed, the colors of all the squares in that row are inverted; that is, white squares become black and vice versa. When a button attached to a column is pressed, the colors of all the squares in that column are inverted. Takahashi can freely press the buttons any number of times. Determine whether he can have exactly $K$ black squares in the grid. ## Constraints * $1 \leq N,M \leq 1000$ * $0 \leq K \leq NM$ ## Input Input is given from Standard Input in the following format: $N$ $M$ $K$ [samples]

Samples

Input #1

2 2 2

Output #1

Yes

Press the buttons in the order of the first row, the first column.

Input #2

2 2 1

Output #2

No

Input #3

3 5 8

Output #3

Yes

Press the buttons in the order of the first column, third column, second row, fifth column.

Input #4

7 9 20

Output #4

No

API Response (JSON)

{
  "problem": {
    "name": "fLIP",
    "description": {
      "content": "We have a grid with $N$ rows and $M$ columns of squares. Initially, all the squares are white. There is a button attached to each row and each column. When a button attached to a row is pressed, the c",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "code_festival_2017_quala_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a grid with $N$ rows and $M$ columns of squares. Initially, all the squares are white.\nThere is a button attached to each row and each column. When a button attached to a row is pressed, the c...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments