<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) {

        unordered_map<long, unsigned int> dp;

        return findPathUtil(m,n, maxMove, startRow, startColumn, 0, dp);
        
    }

    unsigned int findPathUtil(int m, int n, int maxMove, int row, int column, int numMoves, unordered_map<long, unsigned int>& dp) {
        if(numMoves > maxMove) {
            return 0;
        }
        if(row<0 || column<0 || row>=m || column>=n) {
            return 1;
        }
        if(dp.find(row*10000 + column*100 + numMoves)  != dp.end()) {
            return dp[row*10000 + column*100 + numMoves];
        }

        dp[row*10000 + column*100 + numMoves] = (findPathUtil(m,n,maxMove, row+1, column, numMoves+1, dp) +
                                        findPathUtil(m,n,maxMove, row-1, column, numMoves+1, dp) +
                                        findPathUtil(m,n,maxMove, row, column+1, numMoves+1, dp) +
                                        findPathUtil(m,n,maxMove, row, column - 1, numMoves+1, dp)) % 1000000007;

        return dp[row*10000 + column*100 + numMoves]% 1000000007;
    }
};
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