<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:
        n, m = m, n
        dp = [[[0]*(maxMove+1) for i in range(m+2)] for j in range(n+2)]
        mod = 10**9+7
        startRow += 1
        startColumn += 1
        dp[startRow][startColumn][0] = 1
        for k in range(1, maxMove+1):
            for i in range(n+2):
                for j in range(m+2):
                    dx = [0, 0, -1, 1]
                    dy = [-1, 1, 0, 0]
                    for x in range(4):
                        tx = dx[x] + i
                        ty = dy[x] + j

                        if tx <= 0 or ty <= 0:
                            continue
                        if tx >= n+1 or ty >= m+1:
                            continue
                        
      
                        dp[i][j][k] += dp[tx][ty][k-1]
                        dp[i][j][k] %= mod

        res = 0
        for i in range(n+2):
            for j in range(m+2):
                for k in range(maxMove+1):
                    if i == 0 or j == 0 or i == n+1 or j == m+1:

                        res += dp[i][j][k]
                        res %= mod
        return res



18500