<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 MOD = 1e9 + 7;
    unordered_map<string, int> dp;

    int solve(int m, int n, int maxmove, int i, int j) {
        if (min(i, j) < 0 || i >= m || j >= n) return 1;
        if (maxmove == 0) return 0;

        string key = to_string(i) + "-" + to_string(j) + "-" + to_string(maxmove);
        if (dp.count(key)) return dp[key];

        int cnt = 0;
        cnt = (cnt + solve(m, n, maxmove - 1, i + 1, j)) % MOD;
        cnt = (cnt + solve(m, n, maxmove - 1, i - 1, j)) % MOD;
        cnt = (cnt + solve(m, n, maxmove - 1, i, j + 1)) % MOD;
        cnt = (cnt + solve(m, n, maxmove - 1, i, j - 1)) % MOD;

        return dp[key] = cnt;
    }

    int findPaths(int m, int n, int maxMove, int i, int j) {
        return solve(m, n, maxMove, i, j);
    }
};

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