<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 {
    const int MOD = 1000000007;

public:
    int numWays(int steps, int arrLen) {
        vector<unordered_map<int, long long>> vec(steps);
        unordered_map<int, long long> mp, tp;
        mp[0] = 1;
        if(arrLen > 1)
        mp[1] = 1;
        vec[0] = mp;
        for(int i = 1; i < steps; i++){
            mp.clear();
            tp = vec[i-1];
            for(auto it = tp.begin(); it != tp.end(); it++){
                int el = it->first;
                if(el + 1 < arrLen) mp[el+1] = (mp[el+1] + it->second) % MOD;
                if(el - 1 >= 0) mp[el-1] = (mp[el-1] + it->second) % MOD;
                mp[el] = (mp[el] + it->second) % MOD;
            }
            vec[i] = mp;
        }
        return (int)vec[steps - 1][0];
    }
};
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