<p>There is an <code>m x n</code> grid with a ball. The ball is initially at the position <code>[startRow, startColumn]</code>. You are allowed to move the ball to one of the four adjacent cells in the grid (possibly out of the grid crossing the grid boundary). You can apply <strong>at most</strong> <code>maxMove</code> moves to the ball.</p>

<p>Given the five integers <code>m</code>, <code>n</code>, <code>maxMove</code>, <code>startRow</code>, <code>startColumn</code>, return the number of paths to move the ball out of the grid boundary. Since the answer can be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/28/out_of_boundary_paths_1.png" style="width: 500px; height: 296px;" />
<pre>
<strong>Input:</strong> m = 2, n = 2, maxMove = 2, startRow = 0, startColumn = 0
<strong>Output:</strong> 6
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/28/out_of_boundary_paths_2.png" style="width: 500px; height: 293px;" />
<pre>
<strong>Input:</strong> m = 1, n = 3, maxMove = 3, startRow = 0, startColumn = 1
<strong>Output:</strong> 12
</pre>

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

<ul>
	<li><code>1 &lt;= m, n &lt;= 50</code></li>
	<li><code>0 &lt;= maxMove &lt;= 50</code></li>
	<li><code>0 &lt;= startRow &lt; m</code></li>
	<li><code>0 &lt;= startColumn &lt; n</code></li>
</ul>

class Solution:
    def findPaths(self, m: int, n: int, maxMove: int, startRow: int, startColumn: int) -> int:
        dp = [[[-1 for _ in range(n)] for _ in range(m)] for _ in range (maxMove+1)]
        dx = [-1, 0, 1, 0]
        dy = [0, 1, 0, -1]
    

        def dfs(x: int, y: int, maxMove: int) -> int:
            if maxMove == 0:
                return 0

            print(maxMove, x, y)
            if dp[maxMove][x][y] != -1:
                return dp[maxMove][x][y]

            val = 0

            for k in range(4):
                u = x + dx[k]
                v = y + dy[k]
                if isInside(u, v) == False:
                    val += 1
                    continue
                
                val += dfs(u, v, maxMove - 1)
                val %= (10**9 + 7)

            dp[maxMove][x][y] = val
            return val
                

        def isInside(x: int, y: int) -> bool:
            return (x >= 0 and x < m) and (y >= 0 and y < n)

        return int(dfs(startRow, startColumn, maxMove))
19900