<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 numRollsToTarget(int n, int k, int target) {
        std::vector<std::vector<uint64_t>> targets(n+1, std::vector<uint64_t>(1001, 0));
        targets[0][0] = 1;

        // for each dice
        for(int dice=1; dice<=n; ++dice) {
            for(int face=1; face<=k; ++face) {
                for(int i=face; i<targets[dice].size(); ++i) {
                    //targets[dice][i] += (targets[dice-1][i-face]);
                    targets[dice][i] = (targets[dice][i] + targets[dice-1][i-face]) % static_cast<uint64_t>(1e9 + 7);
                }
            }
        }

       return targets[n][target] % static_cast<uint64_t>(1e9 + 7);
    }


    int dp(int dice, int sides, int target) {
        if(dice == 1 && target <= sides)
        {
            return 1;
        }

        if(dice < 2) {
            return 0;
        }

        int64_t sum = 0;
        for(int i=1; i<=sides; ++i) {
            sum += dp(dice-1, sides, target-i);
        }

        return sum;
    }
};
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