<p>You have a pointer at index <code>0</code> in an array of size <code>arrLen</code>. At each step, you can move 1 position to the left, 1 position to the right in the array, or stay in the same place (The pointer should not be placed outside the array at any time).</p>

<p>Given two integers <code>steps</code> and <code>arrLen</code>, return the number of ways such that your pointer is still at index <code>0</code> after <strong>exactly</strong> <code>steps</code> steps. Since the answer may be too 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>

<pre>
<strong>Input:</strong> steps = 3, arrLen = 2
<strong>Output:</strong> 4
<strong>Explanation: </strong>There are 4 differents ways to stay at index 0 after 3 steps.
Right, Left, Stay
Stay, Right, Left
Right, Stay, Left
Stay, Stay, Stay
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> steps = 2, arrLen = 4
<strong>Output:</strong> 2
<strong>Explanation:</strong> There are 2 differents ways to stay at index 0 after 2 steps
Right, Left
Stay, Stay
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> steps = 4, arrLen = 2
<strong>Output:</strong> 8
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= steps &lt;= 500</code></li>
	<li><code>1 &lt;= arrLen &lt;= 10<sup>6</sup></code></li>
</ul>

class Solution {
    int N;
    int M=1e9+7;
    vector<vector<int>> dp;
    unordered_map<string, int> m;
    int check(int steps, int ind){
        if(steps==0){
            if(ind==0)  return 1;
            return 0;
        }
        if(ind>=500)    return 0;
        //string str=to_string(steps)+'_'+to_string(ind);
        if(dp[steps][ind]!=-1)  return dp[steps][ind];
        //if(m.count(str))    return m[str];
        int n1=0, n2=0, n3=0;
        if(ind>0)   n1=check(steps-1, ind-1);
        if(ind<N-1) n2=check(steps-1, ind+1);
        n3=check(steps-1, ind);
        return dp[steps][ind]=((n1+n2)%M+n3)%M;
    }
public:
    int numWays(int steps, int arrLen) {
        N=arrLen;
        dp.resize(501, vector<int>(501, -1));
        return check(steps, 0);
    }
};
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