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leetcode/problem/number-of-dice-rolls-with-target-sum.html

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+<p>You have <code>n</code> dice and each die 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>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>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>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>