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leetcode-problemset/leetcode-cn/originData/number-of-dice-rolls-with-target-sum.json
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{
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"question": {
"questionId": "1263",
"questionFrontendId": "1155",
"categoryTitle": "Algorithms",
"boundTopicId": 19371,
"title": "Number of Dice Rolls With Target Sum",
"titleSlug": "number-of-dice-rolls-with-target-sum",
"content": "<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>\n\n<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>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 1, k = 6, target = 3\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> You throw one die with 6 faces.\nThere is only one way to get a sum of 3.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 2, k = 6, target = 7\n<strong>Output:</strong> 6\n<strong>Explanation:</strong> You throw two dice, each with 6 faces.\nThere are 6 ways to get a sum of 7: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 30, k = 30, target = 500\n<strong>Output:</strong> 222616187\n<strong>Explanation:</strong> The answer must be returned modulo 10<sup>9</sup> + 7.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n, k &lt;= 30</code></li>\n\t<li><code>1 &lt;= target &lt;= 1000</code></li>\n</ul>\n",
"translatedTitle": "掷骰子等于目标和的方法数",
"translatedContent": "<p>这里有&nbsp;<code>n</code>&nbsp;个一样的骰子,每个骰子上都有&nbsp;<code>k</code>&nbsp;个面,分别标号为&nbsp;<code>1</code>&nbsp;到 <code>k</code> 。</p>\n\n<p>给定三个整数 <code>n</code>、<code>k</code> 和 <code>target</code>,请返回投掷骰子的所有可能得到的结果(共有 <code>k<sup>n</sup></code> 种方式),使得骰子面朝上的数字总和等于 <code>target</code>。</p>\n\n<p>由于答案可能很大,你需要对 <code>10<sup>9</sup> + 7</code> <strong>取模</strong>。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<pre>\n<strong>输入:</strong>n = 1, k = 6, target = 3\n<strong>输出:</strong>1\n<strong>解释:</strong>你掷了一个有 6 个面的骰子。\n得到总和为 3 的结果的方式只有一种。\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre>\n<strong>输入:</strong>n = 2, k = 6, target = 7\n<strong>输出:</strong>6\n<strong>解释:</strong>你掷了两个骰子,每个骰子有 6 个面。\n有 6 种方式得到总和为 7 的结果: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1。\n</pre>\n\n<p><strong>示例 3</strong></p>\n\n<pre>\n<strong>输入:</strong>n = 30, k = 30, target = 500\n<strong>输出:</strong>222616187\n<strong>解释:</strong>返回的结果必须对 10<sup>9</sup> + 7 取模。</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n, k &lt;= 30</code></li>\n\t<li><code>1 &lt;= target &lt;= 1000</code></li>\n</ul>\n",
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