<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>

typedef long long int ll;
class Solution {
public:
int mod=1e9+7;
    vector<vector<ll>> dir={{0,1},{1,0},{0,-1},{-1,0}};
    ll t[51][51][51];
    ll f(ll i,ll j,ll row,ll col,ll moves)
    {
        if( i<0 || j<0 || i>=row || j>=col) return 1;
        if(moves==0) return 0;
        ll ct=0;
        if(t[i][j][moves]!=-1) return t[i][j][moves];
        // if(!vis[i][j]) return 0;
        // vis[i][j]=1;
        for(ll m=0;m<4;m++)
        {
            ll newr=i+dir[m][0];
            ll newc=j+dir[m][1];
           
            ct=( ct%mod+ f(newr,newc,row,col,moves-1)%mod)%mod;
        }
        // vis[i][j]=0;
        return t[i][j][moves]=ct;
        
    }
    ll findPaths(ll m, ll n, ll maxMove, ll startRow, ll startColumn) {
     
        memset(t,-1,sizeof(t));
         return f(startRow,startColumn,m,n,maxMove);
    }
};
8956