<p>You are given two integers <code>m</code> and <code>n</code>, which represent the dimensions of a matrix.</p>

<p>You are also given the <code>head</code> of a linked list of integers.</p>

<p>Generate an <code>m x n</code> matrix that contains the integers in the linked list presented in <strong>spiral</strong> order <strong>(clockwise)</strong>, starting from the <strong>top-left</strong> of the matrix. If there are remaining empty spaces, fill them with <code>-1</code>.</p>

<p>Return <em>the generated matrix</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/05/09/ex1new.jpg" style="width: 240px; height: 150px;" />
<pre>
<strong>Input:</strong> m = 3, n = 5, head = [3,0,2,6,8,1,7,9,4,2,5,5,0]
<strong>Output:</strong> [[3,0,2,6,8],[5,0,-1,-1,1],[5,2,4,9,7]]
<strong>Explanation:</strong> The diagram above shows how the values are printed in the matrix.
Note that the remaining spaces in the matrix are filled with -1.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/05/11/ex2.jpg" style="width: 221px; height: 60px;" />
<pre>
<strong>Input:</strong> m = 1, n = 4, head = [0,1,2]
<strong>Output:</strong> [[0,1,2,-1]]
<strong>Explanation:</strong> The diagram above shows how the values are printed from left to right in the matrix.
The last space in the matrix is set to -1.</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= m, n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= m * n &lt;= 10<sup>5</sup></code></li>
	<li>The number of nodes in the list is in the range <code>[1, m * n]</code>.</li>
	<li><code>0 &lt;= Node.val &lt;= 1000</code></li>
</ul>

# Definition for singly-linked list.
# class ListNode:
#     def __init__(self, val=0, next=None):
#         self.val = val
#         self.next = next
class Solution:
    def spiralMatrix(self, m: int, n: int, head: Optional[ListNode]) -> List[List[int]]:
        x, y = 0, 0
        EAST, SOUTH, WEST, NORTH = 0, 1, 2, 3
        direction = EAST
        filled_coords = set()

        matrix = [[-1 for _ in range(n)] for _ in range(m)]
        offset_map = {
            EAST: (0, 1), SOUTH: (1, 0),
            WEST: (0, -1), NORTH: (-1, 0)
        }

        def is_filled(y, x):
            if (y, x) in filled_coords:
                # print('FILLED')
                return True

            out_of_bounds = (
                (x < 0) or (y < 0) or
                (x >= n) or (y >= m)
            )
            # print('OOB', out_of_bounds, (y, x), (m, n))
            return out_of_bounds

        turns = 0
        while head is not None:
            # print('--------------')
            # print('HEAD', head.val, (y, x))
            dy, dx = offset_map[direction]
            ny, nx = y + dy, x + dx

            if is_filled(ny, nx):
                if turns > 4:
                    matrix[y][x] = head.val
                    break

                # print('ROTATE', direction)
                direction = (direction + 1) % 4
                turns += 1
                continue

            turns = 0
            filled_coords.add((y, x))
            # print('FILLED', filled_coords)
            matrix[y][x] = head.val
            head = head.next
            y, x = ny, nx

        return matrix
            
            
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