<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]]:
        left, right = 0, n - 1
        top, bottom = 0, m - 1

        grid = [[-1] * n for _ in range(m)]
        directions = [(1, 0), (0, 1), (-1, 0), (0, -1)]  # right, down, left, top

        r, c = 0, 0  # current row, col
        cur = head  # traverser
        d = 0  # current direction (for traverser)
        dx, dy = directions[0]  # direction offset (for traverser)

        def change_direction():
            """update dx, dy offset for current direction d"""
            nonlocal d, dx, dy
            d = (d + 1) % 4
            # dx -> horizontal, dy -> vertical
            dx, dy = directions[d]

        def is_in_bound(i, j):
            """check if (i, j) is within boundaries defined by top, right, bottom, left"""
            vertical_constraints = top <= i <= bottom
            horizontal_constraints = left <= j <= right
            return vertical_constraints and horizontal_constraints

        while cur:
            # Fill value
            grid[r][c] = cur.val
            cur = cur.next

            # check if next step is in boundary
            if not is_in_bound(r + dy, c + dx):
                # inorder to avoid repeating of top-left (whilst traversing last direction)
                if d == 0:
                    # first direction
                    # (ie top-border) traversed (hence top-left is accounted)
                    # So shrink just top pointer to next possible top-row
                    top += 1
                elif d == 3:
                    # last direction
                    # hence shrink the boundaries (come inwards)
                    left, right, bottom = left + 1, right - 1, bottom - 1

                change_direction()

            # move ahead
            r, c = r + dy, c + dx

        return grid
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