<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 MOD = 1e9+7;

    int calculate(int currIndex, int arrLen, int stepsLeft, vector<vector<long long>> &dp){
        if(stepsLeft==0){
            if(currIndex==0){
                return 1;
            }
            return 0;
        }
        if(dp[currIndex][stepsLeft]!=-1){
            return dp[currIndex][stepsLeft];
        }
        int left=0,right=0,stay=0;
        if(currIndex > 0){
            left = calculate(currIndex-1, arrLen, stepsLeft-1, dp);
        }
        if(currIndex<arrLen-1){
            right = calculate(currIndex+1, arrLen, stepsLeft-1, dp);
        }
        stay = calculate(currIndex, arrLen, stepsLeft-1, dp);

        long long ans = ((left+right)%MOD+stay)%MOD;
        return dp[currIndex][stepsLeft] = ans;
    }

    

    int numWays(int steps, int arrLen) {
        vector<vector<long long>> dp(511, vector<long long>(steps+1,0));
        //return calculate(0, arrLen, steps, dp);
        dp[0][0] = 1;
        for(int j=1;j<=steps;j++){
            for(int i = 509;i>=0;i--){
                int left=0,right=0,stay=0;
                if(i > 0){
                    left = dp[i-1][j-1];
                }
                if(i<arrLen-1){
                    right = dp[i+1][j-1];
                }
                stay = dp[i][j-1];

                long long ans = ((left+right)%MOD+stay)%MOD;
                dp[i][j] = ans;
            }
        }
        return dp[0][steps];
    }
};
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