<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;
    int ans = 0;
    void f(int m, int n, int maxMove, int startRow, int startCol) {
        if (maxMove < 0)
            return;
        if (startRow >= m || startCol >= n || startRow < 0 || startCol < 0) {
            ans=(ans+1)%mod;
            return;
        }
        f(m, n, maxMove - 1, startRow, startCol + 1);
        f(m, n, maxMove - 1, startRow, startCol - 1);
        f(m, n, maxMove - 1, startRow + 1, startCol);
        f(m, n, maxMove - 1, startRow - 1, startCol);
    }
    int findPaths(int m, int n, int maxMove, int startRow, int startCol) {
        f(m, n, maxMove, startRow, startCol);
        return ans % mod;
    }
    */
    int mod = 1e9 + 7;

   vector<vector< int>> directions={{1,0},{0,1},{-1,0},{0,-1}};
    
    int findPaths(int m, int n, int maxMove, int startRow, int startCol) {
        vector<vector<int>>t(50,vector<int>(50,0));
        t[startRow][startCol]=1;
        int res=0;
        for(int k=1;k<=maxMove;k++){
        vector<vector<int>>temp(50,vector<int>(50,0));
        for(int i=0;i<m;i++){
             for(int j=0;j<n;j++){
                for(auto & dir: directions){
                    int x=i+dir[0];
                    int y=j+dir[1];
                    if(x<0||x>=m||y<0||y>=n){
                        res=(res+t[i][j])%mod;
                    }
                    else{
                        temp[x][y]=(temp[x][y]+t[i][j])%mod;
                    }

                }

            
        }



        }
        t=temp;


        }
        return res;
    }
};
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