<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:
    
    // long long int solve(int steps, int arrLen,int i,vector<vector<long long int>> &dp)
    // {
    //     if(i>=arrLen||i<0)
    //     return 0;
    //     if(steps==0)
    //     {
    //         if(i==0)
    //         return 1;
    //         return 0;
    //     }
    //     long long int mo=1e9+7;
    //     if(dp[steps][i]!=-1)
    //     return dp[steps][i];
    //     long long int ans=0;
    //     ans+=solve(steps-1,arrLen,i,dp);
    //     ans+=solve(steps-1,arrLen,i-1,dp);
    //     ans+=solve(steps-1,arrLen,i+1,dp);
    //     return dp[steps][i]=ans%mo;
    // }
    int numWays(int steps, int arrLen) {
        if(arrLen>steps+1)
        arrLen=steps+1;
        vector<vector<long long int>> dp(steps+1,vector<long long int>(arrLen+1,0));
        dp[0][0]=1;
        long long int mo=1e9+7;
        for(int i=1;i<=steps;i++)
        {
           for(int j=0;j<arrLen;j++)
           {
              if(j!=0)
              dp[i][j]+=dp[i-1][j-1]%mo;
              if(j!=arrLen-1)
              dp[i][j]+=dp[i-1][j+1]%mo;
              dp[i][j]+=dp[i-1][j]%mo;
              
           }
        }
        return int(dp[steps][0])%mo;
    }
};
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