<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>

const int mod = 1e9+7;
class Solution {
public:
    int mTmp, nTmp, maxMoveTmp;
    vector<vector<vector<int>>> dp;
    int recur(int i, int j, int move=0){
        if(move > maxMoveTmp) return 0;
        if(i < 0 || i >= mTmp || j < 0 || j >= nTmp) return 1;
        if(dp[i][j][move] != -1) return dp[i][j][move];

        int ans = 0;
        vector<int> idxs = {0, -1, 0, 1, 0};
        for(int k=0; k<4; ++k){
            int nI = i+idxs[k], nJ = j+idxs[k+1];
            ans = (0LL + ans + recur(nI, nJ, move+1))%mod;
        }

        return dp[i][j][move] = ans;
    }

    int findPaths(int m, int n, int maxMove, int startRow, int startCol) {
        mTmp = m, nTmp = n, maxMoveTmp = maxMove;
        dp.resize(m, vector<vector<int>>(n, vector<int>(maxMove+1, -1)));
        return recur(startRow, startCol);
    }
};
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