<p>You have <code>n</code> dice, and each dice has <code>k</code> faces numbered from <code>1</code> to <code>k</code>.</p>

<p>Given three integers <code>n</code>, <code>k</code>, and <code>target</code>, return <em>the number of possible ways (out of the </em><code>k<sup>n</sup></code><em> total ways) </em><em>to roll the dice, so the sum of the face-up numbers equals </em><code>target</code>. 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> n = 1, k = 6, target = 3
<strong>Output:</strong> 1
<strong>Explanation:</strong> You throw one die with 6 faces.
There is only one way to get a sum of 3.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 2, k = 6, target = 7
<strong>Output:</strong> 6
<strong>Explanation:</strong> You throw two dice, each with 6 faces.
There are 6 ways to get a sum of 7: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 30, k = 30, target = 500
<strong>Output:</strong> 222616187
<strong>Explanation:</strong> The answer must be returned modulo 10<sup>9</sup> + 7.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n, k &lt;= 30</code></li>
	<li><code>1 &lt;= target &lt;= 1000</code></li>
</ul>

class Solution {
public:
    int mod = 1000000007;
    long long getDiceRolls(int n, int k, int target,
                           vector<vector<long long>>& dp) {
        if (n < 0)
            return 0;
        if (target < 0)
            return 0;
        if (n == 0 && target == 0)
            return 1;
        if ((n != 0 && target == 0) || (n == 0 && target != 0))
            return 0;

        if (dp[n][target] != -1)
            return dp[n][target];

        long long ways = 0;
        for (int i = 1; i <= k; i++) {
            ways = ((ways % mod) +
                    (getDiceRolls(n - 1, k, target - i, dp) % mod)) %
                   mod;
        }

        return dp[n][target] = ways;
    }
    int numRollsToTarget(int n, int k, int target) {
        vector<vector<long long>> dp(n + 1, vector<long long>(target + 1, 0));

        // Initialize base case where no dice is used
        
        dp[0][0] = 1;
      
        for (int index = 1; index <= n; index++) {
            for (int t = 1; t <= target; t++) {
                long long ways = 0;
                for (int i = 1; i <= k; i++) {
                    if (t - i >= 0) {
                        ways = (ways + dp[index - 1][t - i]) % mod;
                    }
                }
                dp[index][t] = ways;
            }
        }

        cout << "DP Table : " << endl;
        for (auto i : dp) {
            for (auto j : i) {
                cout << j << " ";
            }
            cout << endl;
        }
        cout << endl;

        return dp[n][target];
    }
};
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