<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 dp[55][55][55];
int rec(int i,int j,int move,int n,int m){
    if(i<0 || j<0 || i>=m || j>=n)return 1; 
    if(move==0)return 0;
    if(dp[i][j][move]!=-1)return dp[i][j][move];
    int sum=0;
    vector<int>dx={1,-1,0,0},dy={0,0,1,-1};
    if(move>=1){
        for(int k=0;k<4;++k){
            int ni=i+dx[k],nj=j+dy[k];
            sum+=rec(ni,nj,move-1,n,m)%1000000007;
            sum%=1000000007;
        }
    }
    return dp[i][j][move]=sum%1000000007;
}
    int findPaths(int m, int n, int maxMove, int startRow, int startColumn) {
        memset(dp,-1,sizeof(dp));
        return rec(startRow,startColumn,maxMove,n,m);
    }
};
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