<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>

int mod=1e9+7;
class Solution {
public:
    long long solve(int x,int y,int m,int n,int times,int maxMove,vector<vector<vector<long long>>>&dp){
        if(x<0 ||y<0 ||x>=m||y>=n)
            return 1;
        if(times>=maxMove){
            return 0;
        }
        if(dp[x][y][times]!=-1)
            return (dp[x][y][times])%mod;
       return  dp[x][y][times]=(solve(x-1,y,m,n,times+1,maxMove,dp)%mod+solve(x,y-1,m,n,times+1,maxMove,dp)%mod+solve(x+1,y,m,n,times+1,maxMove,dp)%mod+
        solve(x,y+1,m,n,times+1,maxMove,dp)%mod)%mod;
    }
    int findPaths(int m, int n, int maxMove, int startRow, int startColumn) {
        vector<vector<vector<long long>>>dp(m+1,vector<vector<long long>>(n+1,vector<long long>(maxMove+1,-1)));
        return solve(startRow,startColumn,m,n,0,maxMove,dp);
    }
};
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