<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>

int mod=1e9+7;
class Solution {
public:
    map<pair<int,int>,int>mp;
    int help(int level,int steps,int arrLen)
    {
        if(steps==0)
        {
            if(level==0)return 1;
            else return 0;
        }
        if(mp.find({level,steps})!=mp.end())return mp[{level,steps}];
        long long ans=0;
        if(level+1<arrLen)ans=(ans+help(level+1,steps-1,arrLen))%mod;
        if(level-1>=0)ans=(ans+help(level-1,steps-1,arrLen))%mod;
        if(level<arrLen && level>=0)ans=(ans+help(level,steps-1,arrLen))%mod;

        return mp[{level,steps}]=ans%mod;
    }
    int numWays(int steps, int arrLen) {
        return help(0,steps,arrLen);
    }
};
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