<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 {
public:
    int generate(const int &arrLen, const int &endPos, const int &k, int i, int pos)
    {
        if (i == k)
        {
            return endPos == pos;
        }
        int x1 = 0;
        if ((pos + 1) != arrLen)
        {
            auto it = hash.find((100000*(pos + 1) + i + 1));
            if (it == hash.cend())
            {
                hash[(100000*(pos + 1) + i + 1)] = generate(arrLen, endPos, k, i + 1, pos + 1);
            }
            x1 = hash[(100000*(pos + 1) + i + 1)] % 1000000007;
        }
        int x2 = 0;
        if ((pos - 1) >= 0)
        {
            auto it = hash.find(100000*(pos - 1) + i + 1);
            if (it == hash.cend())
            {
                hash[(100000*(pos - 1) + i + 1)] = generate(arrLen, endPos, k, i + 1, pos - 1);
            }
            x2 = hash[(100000*(pos - 1) + i + 1)] % 1000000007;
        }
        auto it = hash.find(100000*(pos) + i + 1);
        if (it == hash.cend())
        {
            hash[(100000*(pos) + i + 1)] = generate(arrLen, endPos, k, i + 1, pos);
        }
        int x3 = hash[(100000*(pos) + i + 1)] % 1000000007; 
        return (static_cast<long long>(x1) + x2 + x3) % 1000000007;
    }


    int numWays(int steps, int arrLen) {
        //hash.resize(arrLen + 1);
        //for (auto &e: hash)
        //{
        //    e.resize(steps + 1, INT_MAX);
        //}
        return generate(arrLen, 0, steps, 0, 0);
    }
private:
    unordered_map<int, int> hash;
    //vector<vector<int>> hash;
};
49256