<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 {
    int modu=1e9+7;
    int ans=0;
    int f(int m, int n, int mm, int sR, int sC,vector<vector<vector<int>>> &dp)
    {   
        int sum=0;
        if(sR<0 || sR>=m || sC<0 || sC>=n)
        {
            return 1;
        }
        if(dp[sR][sC][mm]!=-1) return dp[sR][sC][mm]%modu;
        if(mm!=0)
        {
        vector<int> dr={0,1,0,-1};
        vector<int> dc={1,0,-1,0};
        for(int i=0;i<4;i++)
        {
            sum=(sum%modu+f(m,n,mm-1,sR+dr[i],sC+dc[i],dp)%modu)%modu;
        }
        sum=sum%modu;
        }
        return dp[sR][sC][mm]=sum%modu;
    }
public:
    int findPaths(int m, int n, int mm, int sR, int sC) {
    vector<vector<vector<int>>> dp(m+1,vector<vector<int>>(n+1,vector<int> (mm+1,-1)));    
    return f(m,n,mm,sR,sC,dp)%modu;
    
    }
};
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