<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 n, m;

int mod = 1e9+7;
    int dfs(int cr, int cc, int maxmoves, vector<vector<vector<long long>>>& cache){
        if(cr >= n || cc >= m || cr < 0 || cc < 0) return 1;

        if(maxmoves <= 0) return 0;

        if(cache[cr][cc][maxmoves] != -1) return cache[cr][cc][maxmoves];

        long long total = 0;
        total += dfs(cr+1, cc, maxmoves-1, cache);
        total += dfs(cr-1, cc, maxmoves-1, cache);
        total += dfs(cr, cc+1, maxmoves-1, cache);
        total += dfs(cr, cc-1, maxmoves-1, cache);

        cache[cr][cc][maxmoves] = total%mod;
        cout<<" "<<cr<<" "<<cc<<" "<<maxmoves<<" "<<total<<endl;

        return total%mod;
    }

    int findPaths(int a, int b, int maxMove, int startRow, int startColumn) {
        n = a;
        m = b;

        vector<vector<vector<long long>>> cache(n, vector<vector<long long>>(m, vector<long long>(maxMove+1, -1)));

        return dfs(startRow, startColumn, maxMove, cache);
    }
};
12451