<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:
        if not maxMove:
            return 0
        total_ways = 0
        MOD = int(1e9) + 7
        ways = [[[0, 0] for _ in range(n)] for _ in range(m)]
        ways[startRow][startColumn][0] = 1
        prev = 0
        for current_move in range(maxMove - 1):
            for row in range(m):
                for column in range(n):
                    if row == 0:
                        total_ways = (total_ways + ways[row][column][prev])
                    if column == 0:
                        total_ways = (total_ways + ways[row][column][prev])
                    if row == m - 1:
                        total_ways = (total_ways + ways[row][column][prev])
                    if column == n - 1:
                        total_ways = (total_ways + ways[row][column][prev])
                    total_ways %= MOD
                    current_ways = 0
                    if row > 0:
                        current_ways += ways[row - 1][column][prev]
                    if column > 0:
                        current_ways += ways[row][column - 1][prev]
                    if row + 1 < m:
                        current_ways += ways[row + 1][column][prev]
                    if column + 1 < n:
                        current_ways += ways[row][column + 1][prev]
                    current_ways %= MOD
                    ways[row][column][1 ^ prev] = current_ways
            prev ^= 1
        for row in range(m):
            total_ways = (total_ways + ways[row][0][prev])
            total_ways = (total_ways + ways[row][n - 1][prev])
        for column in range(n):
            total_ways = (total_ways + ways[0][column][prev])
            total_ways = (total_ways + ways[m - 1][column][prev])
        return total_ways % MOD
17200