<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 {
public:
    int findPaths(int m, int n, int maxMove, int startRow, int startColumn) {
        vector<vector<vector<int>>> dp(maxMove+1, vector<vector<int>>(m+2, vector<int>(n+2, 0)));
        int den = pow(10,9) + 7;
        for(int i=0; i<=maxMove; ++i) {
            for(int j=0; j<m+2; ++j) {
                dp[i][j][0] = 1;
                dp[i][j][n+1] = 1;
            }
            for(int j=0; j<n+2; ++j) {
                dp[i][0][j] = 1;
                dp[i][m+1][j] = 1;
            }
        }

        for(int move=1; move<=maxMove; ++move) {
            for(int i=0; i<m; ++i) {
                for(int j=0; j<n; ++j) {
                    dp[move][i+1][j+1] += dp[move-1][i+1][j];
                    dp[move][i+1][j+1] %= den;
                    dp[move][i+1][j+1] += dp[move-1][i+1][j+2];
                    dp[move][i+1][j+1] %= den;
                    dp[move][i+1][j+1] += dp[move-1][i][j+1];
                    dp[move][i+1][j+1] %= den;
                    dp[move][i+1][j+1] += dp[move-1][i+2][j+1];
                    dp[move][i+1][j+1] %= den;
                }
            }
        }

        return dp[maxMove][startRow+1][startColumn+1];
    }
};
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