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            "questionFrontendId": "3179",
            "categoryTitle": "Algorithms",
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            "title": "Find the N-th Value After K Seconds",
            "titleSlug": "find-the-n-th-value-after-k-seconds",
            "content": "<p>You are given two integers <code>n</code> and <code>k</code>.</p>\n\n<p>Initially, you start with an array <code>a</code> of <code>n</code> integers where <code>a[i] = 1</code> for all <code>0 &lt;= i &lt;= n - 1</code>. After each second, you simultaneously update each element to be the sum of all its preceding elements plus the element itself. For example, after one second, <code>a[0]</code> remains the same, <code>a[1]</code> becomes <code>a[0] + a[1]</code>, <code>a[2]</code> becomes <code>a[0] + a[1] + a[2]</code>, and so on.</p>\n\n<p>Return the <strong>value</strong> of <code>a[n - 1]</code> after <code>k</code> seconds.</p>\n\n<p>Since the answer may be very 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<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">n = 4, k = 5</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">56</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<table border=\"1\">\n\t<tbody>\n\t\t<tr>\n\t\t\t<th>Second</th>\n\t\t\t<th>State After</th>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>0</td>\n\t\t\t<td>[1,1,1,1]</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>[1,2,3,4]</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>[1,3,6,10]</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>3</td>\n\t\t\t<td>[1,4,10,20]</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>4</td>\n\t\t\t<td>[1,5,15,35]</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>5</td>\n\t\t\t<td>[1,6,21,56]</td>\n\t\t</tr>\n\t</tbody>\n</table>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">n = 5, k = 3</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">35</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<table border=\"1\">\n\t<tbody>\n\t\t<tr>\n\t\t\t<th>Second</th>\n\t\t\t<th>State After</th>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>0</td>\n\t\t\t<td>[1,1,1,1,1]</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>[1,2,3,4,5]</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>[1,3,6,10,15]</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>3</td>\n\t\t\t<td>[1,4,10,20,35]</td>\n\t\t</tr>\n\t</tbody>\n</table>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n, k &lt;= 1000</code></li>\n</ul>\n",
            "translatedTitle": "K 秒后第 N 个元素的值",
            "translatedContent": "<p>给你两个整数 <code>n</code> 和 <code>k</code>。</p>\n\n<p>最初，你有一个长度为 <code>n</code> 的整数数组 <code>a</code>，对所有 <code>0 &lt;= i &lt;= n - 1</code>，都有 <code>a[i] = 1</code> 。每过一秒，你会同时更新每个元素为其前面所有元素的和加上该元素本身。例如，一秒后，<code>a[0]</code> 保持不变，<code>a[1]</code> 变为 <code>a[0] + a[1]</code>，<code>a[2]</code> 变为 <code>a[0] + a[1] + a[2]</code>，以此类推。</p>\n\n<p>返回 <code>k</code> 秒后 <code>a[n - 1]</code> 的<strong>值</strong>。</p>\n\n<p>由于答案可能非常大，返回其对 <code>10<sup>9</sup> + 7</code> <strong>取余 </strong>后的结果。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong><span class=\"example-io\">n = 4, k = 5</span></p>\n\n<p><strong>输出：</strong><span class=\"example-io\">56</span></p>\n\n<p><strong>解释：</strong></p>\n\n<table border=\"1\">\n\t<tbody>\n\t\t<tr>\n\t\t\t<th>时间（秒）</th>\n\t\t\t<th>数组状态</th>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>0</td>\n\t\t\t<td>[1,1,1,1]</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>[1,2,3,4]</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>[1,3,6,10]</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>3</td>\n\t\t\t<td>[1,4,10,20]</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>4</td>\n\t\t\t<td>[1,5,15,35]</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>5</td>\n\t\t\t<td>[1,6,21,56]</td>\n\t\t</tr>\n\t</tbody>\n</table>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong><span class=\"example-io\">n = 5, k = 3</span></p>\n\n<p><strong>输出：</strong><span class=\"example-io\">35</span></p>\n\n<p><strong>解释：</strong></p>\n\n<table border=\"1\">\n\t<tbody>\n\t\t<tr>\n\t\t\t<th>时间（秒）</th>\n\t\t\t<th>数组状态</th>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>0</td>\n\t\t\t<td>[1,1,1,1,1]</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>[1,2,3,4,5]</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>[1,3,6,10,15]</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>3</td>\n\t\t\t<td>[1,4,10,20,35]</td>\n\t\t</tr>\n\t</tbody>\n</table>\n</div>\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;= 1000</code></li>\n</ul>\n",
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