leetcode-problemset/leetcode-cn/originData/number-of-ways-to-earn-points.json

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            "questionId": "2648",
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            "title": "Number of Ways to Earn Points",
            "titleSlug": "number-of-ways-to-earn-points",
            "content": "<p>There is a test that has <code>n</code> types of questions. You are given an integer <code>target</code> and a <strong>0-indexed</strong> 2D integer array <code>types</code> where <code>types[i] = [count<sub>i</sub>, marks<sub>i</sub>]</code> indicates that there are <code>count<sub>i</sub></code> questions of the <code>i<sup>th</sup></code> type, and each one of them is worth <code>marks<sub>i</sub></code> points.</p>\n\n<ul>\n</ul>\n\n<p>Return <em>the number of ways you can earn <strong>exactly</strong> </em><code>target</code><em> points in the exam</em>. Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p><strong>Note</strong> that questions of the same type are indistinguishable.</p>\n\n<ul>\n\t<li>For example, if there are <code>3</code> questions of the same type, then solving the <code>1<sup>st</sup></code> and <code>2<sup>nd</sup></code> questions is the same as solving the <code>1<sup>st</sup></code> and <code>3<sup>rd</sup></code> questions, or the <code>2<sup>nd</sup></code> and <code>3<sup>rd</sup></code> questions.</li>\n</ul>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> target = 6, types = [[6,1],[3,2],[2,3]]\n<strong>Output:</strong> 7\n<strong>Explanation:</strong> You can earn 6 points in one of the seven ways:\n- Solve 6 questions of the 0<sup>th</sup> type: 1 + 1 + 1 + 1 + 1 + 1 = 6\n- Solve 4 questions of the 0<sup>th</sup> type and 1 question of the 1<sup>st</sup> type: 1 + 1 + 1 + 1 + 2 = 6\n- Solve 2 questions of the 0<sup>th</sup> type and 2 questions of the 1<sup>st</sup> type: 1 + 1 + 2 + 2 = 6\n- Solve 3 questions of the 0<sup>th</sup> type and 1 question of the 2<sup>nd</sup> type: 1 + 1 + 1 + 3 = 6\n- Solve 1 question of the 0<sup>th</sup> type, 1 question of the 1<sup>st</sup> type and 1 question of the 2<sup>nd</sup> type: 1 + 2 + 3 = 6\n- Solve 3 questions of the 1<sup>st</sup> type: 2 + 2 + 2 = 6\n- Solve 2 questions of the 2<sup>nd</sup> type: 3 + 3 = 6\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> target = 5, types = [[50,1],[50,2],[50,5]]\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> You can earn 5 points in one of the four ways:\n- Solve 5 questions of the 0<sup>th</sup> type: 1 + 1 + 1 + 1 + 1 = 5\n- Solve 3 questions of the 0<sup>th</sup> type and 1 question of the 1<sup>st</sup> type: 1 + 1 + 1 + 2 = 5\n- Solve 1 questions of the 0<sup>th</sup> type and 2 questions of the 1<sup>st</sup> type: 1 + 2 + 2 = 5\n- Solve 1 question of the 2<sup>nd</sup> type: 5\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> target = 18, types = [[6,1],[3,2],[2,3]]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> You can only earn 18 points by answering all questions.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= target &lt;= 1000</code></li>\n\t<li><code>n == types.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 50</code></li>\n\t<li><code>types[i].length == 2</code></li>\n\t<li><code>1 &lt;= count<sub>i</sub>, marks<sub>i</sub> &lt;= 50</code></li>\n</ul>\n",
            "translatedTitle": "获得分数的方法数",
            "translatedContent": "<p>考试中有 <code>n</code> 种类型的题目。给你一个整数 <code>target</code> 和一个下标从 <strong>0</strong> 开始的二维整数数组 <code>types</code> ，其中 <code>types[i] = [count<sub>i</sub>, marks<sub>i</sub>] </code>表示第 <code>i</code> 种类型的题目有 <code>count<sub>i</sub></code> 道，每道题目对应 <code>marks<sub>i</sub></code> 分。</p>\n\n<p>返回你在考试中恰好得到 <code>target</code> 分的方法数。由于答案可能很大，结果需要对 <code>10<sup>9</sup> +7</code> 取余。</p>\n\n<p><strong>注意</strong>，同类型题目无法区分。</p>\n\n<ul>\n\t<li>比如说，如果有 <code>3</code> 道同类型题目，那么解答第 <code>1</code> 和第 <code>2</code> 道题目与解答第 <code>1</code> 和第 <code>3</code> 道题目或者第 <code>2</code> 和第 <code>3</code> 道题目是相同的。</li>\n</ul>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><strong>输入：</strong>target = 6, types = [[6,1],[3,2],[2,3]]\n<strong>输出：</strong>7\n<strong>解释：</strong>要获得 6 分，你可以选择以下七种方法之一：\n- 解决 6 道第 0 种类型的题目：1 + 1 + 1 + 1 + 1 + 1 = 6\n- 解决 4 道第 0 种类型的题目和 1 道第 1 种类型的题目：1 + 1 + 1 + 1 + 2 = 6\n- 解决 2 道第 0 种类型的题目和 2 道第 1 种类型的题目：1 + 1 + 2 + 2 = 6\n- 解决 3 道第 0 种类型的题目和 1 道第 2 种类型的题目：1 + 1 + 1 + 3 = 6\n- 解决 1 道第 0 种类型的题目、1 道第 1 种类型的题目和 1 道第 2 种类型的题目：1 + 2 + 3 = 6\n- 解决 3 道第 1 种类型的题目：2 + 2 + 2 = 6\n- 解决 2 道第 2 种类型的题目：3 + 3 = 6\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><strong>输入：</strong>target = 5, types = [[50,1],[50,2],[50,5]]\n<strong>输出：</strong>4\n<strong>解释：</strong>要获得 5 分，你可以选择以下四种方法之一：\n- 解决 5 道第 0 种类型的题目：1 + 1 + 1 + 1 + 1 = 5\n- 解决 3 道第 0 种类型的题目和 1 道第 1 种类型的题目：1 + 1 + 1 + 2 = 5\n- 解决 1 道第 0 种类型的题目和 2 道第 1 种类型的题目：1 + 2 + 2 = 5\n- 解决 1 道第 2 种类型的题目：5\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre><strong>输入：</strong>target = 18, types = [[6,1],[3,2],[2,3]]\n<strong>输出：</strong>1\n<strong>解释：</strong>只有回答所有题目才能获得 18 分。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= target &lt;= 1000</code></li>\n\t<li><code>n == types.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 50</code></li>\n\t<li><code>types[i].length == 2</code></li>\n\t<li><code>1 &lt;= count<sub>i</sub>, marks<sub>i</sub> &lt;= 50</code></li>\n</ul>\n",
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