<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:
    long long solve(long long moves,long long m,long long n,long long sr,long long sc,map<pair<pair<long long,long long>,long long>,long long>&dp){
        long long mod=1e9+7;
        if(sr<0 || sr>=m || sc<0 || sc>=n) return 1;
        if(moves==0) return 0;
        if(dp.find({{sr,sc},moves})!=dp.end()) return dp[{{sr,sc},moves}];
        long long delr[]={-1,1,0,0};
        long long delc[]={0,0,-1,1};
        long long ans=0;
        for(long long i=0;i<4;i++){
            ans+=solve(moves-1,m,n,sr+delr[i],sc+delc[i],dp)%mod;
        }
        return dp[{{sr,sc},moves}]=ans%mod;
    }
    long long findPaths(long long m, long long n, long long maxMove, long long startRow, long long startColumn) {
        long long mod=1e9+7;
        map<pair<pair<long long,long long>,long long>,long long>dp;
        return solve(maxMove,m,n,startRow,startColumn,dp)%mod;
    }
};
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