King's Tour

AtCoder

IDabc232_h

Time2000ms

Memory256MB

Difficulty—

We have an $H \times W$ chessboard with $H$ rows and $W$ columns, and a king. Let $(i, j)$ denote the square at the $i$\-th row from the top $(1 \leq i \leq H)$ and $j$\-th column from the left $(1 \leq j \leq W)$. The king can move one square in any direction. Formally, the king on $(i,j)$ can move to $(k,l)$ if and only if $\max(|i-k|,|j-l|) = 1$. A _tour_ is the process of moving the king on the $H \times W$ chessboard as follows. * Start by putting the king on $(1, 1)$. Then, move the king to put it on each square exactly once. For example, when $H = 2, W = 3$, going $(1,1) \to (1,2) \to (1, 3) \to (2, 3) \to (2, 2) \to (2, 1)$ is a valid tour. You are given a square $(a, b)$ other than $(1, 1)$. Construct a tour ending on $(a,b)$ and print it. It can be proved that a solution always exists under the Constraints of this problem. ## Constraints * $2 \leq H \leq 100$ * $2 \leq W \leq 100$ * $1 \leq a \leq H$ * $1 \leq b \leq W$ * $(a, b) \neq (1, 1)$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $H$ $W$ $a$ $b$ [samples]

Samples

Input #1

3 2 3 2

Output #1

1 1
1 2
2 1
2 2
3 1
3 2

The king goes $(1, 1) \to (1, 2) \to (2, 1) \to (2, 2)\to (3, 1) \to (3, 2)$, which is indeed a tour ending on $(3, 2)$.  
There are some other valid tours, three of which are listed below.

*   $(1, 1) \to (1, 2) \to (2, 2) \to (2, 1) \to (3, 1) \to (3, 2)$
*   $(1, 1) \to (2, 1) \to (1, 2) \to (2, 2) \to (3, 1) \to (3, 2)$
*   $(1, 1) \to (2, 2) \to (1, 2) \to (2, 1) \to (3, 1) \to (3, 2)$

API Response (JSON)

{
  "problem": {
    "name": "King's Tour",
    "description": {
      "content": "We have an $H \\times W$ chessboard with $H$ rows and $W$ columns, and a king.   Let $(i, j)$ denote the square at the $i$\\-th row from the top $(1 \\leq i \\leq H)$ and $j$\\-th column from the left $(1 ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc232_h"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have an $H \\times W$ chessboard with $H$ rows and $W$ columns, and a king.  \nLet $(i, j)$ denote the square at the $i$\\-th row from the top $(1 \\leq i \\leq H)$ and $j$\\-th column from the left $(1 ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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