leetcode-problemset/leetcode-cn/originData/find-the-sum-of-the-power-of-all-subsequences.json

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            "questionId": "3345",
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            "categoryTitle": "Algorithms",
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            "title": "Find the Sum of the Power of All Subsequences",
            "titleSlug": "find-the-sum-of-the-power-of-all-subsequences",
            "content": "<p>You are given an integer array <code>nums</code> of length <code>n</code> and a <strong>positive</strong> integer <code>k</code>.</p>\n\n<p>The <strong>power</strong> of an array of integers is defined as the number of <span data-keyword=\"subsequence-array\">subsequences</span> with their sum <strong>equal</strong> to <code>k</code>.</p>\n\n<p>Return <em>the <strong>sum</strong> of <strong>power</strong> of all subsequences of</em> <code>nums</code><em>.</em></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\" style=\"border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;\">\n<p><strong>Input: </strong> <span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\"> nums = [1,2,3], k = 3 </span></p>\n\n<p><strong>Output: </strong> <span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\"> 6 </span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>There are <code>5</code> subsequences of nums with non-zero power:</p>\n\n<ul>\n\t<li>The subsequence <code>[<u><strong>1</strong></u>,<u><strong>2</strong></u>,<u><strong>3</strong></u>]</code> has <code>2</code> subsequences with <code>sum == 3</code>: <code>[1,2,<u>3</u>]</code> and <code>[<u>1</u>,<u>2</u>,3]</code>.</li>\n\t<li>The subsequence <code>[<u><strong>1</strong></u>,2,<u><strong>3</strong></u>]</code> has <code>1</code> subsequence with <code>sum == 3</code>: <code>[1,2,<u>3</u>]</code>.</li>\n\t<li>The subsequence <code>[1,<u><strong>2</strong></u>,<u><strong>3</strong></u>]</code> has <code>1</code> subsequence with <code>sum == 3</code>: <code>[1,2,<u>3</u>]</code>.</li>\n\t<li>The subsequence <code>[<u><strong>1</strong></u>,<u><strong>2</strong></u>,3]</code> has <code>1</code> subsequence with <code>sum == 3</code>: <code>[<u>1</u>,<u>2</u>,3]</code>.</li>\n\t<li>The subsequence <code>[1,2,<u><strong>3</strong></u>]</code> has <code>1</code> subsequence with <code>sum == 3</code>: <code>[1,2,<u>3</u>]</code>.</li>\n</ul>\n\n<p>Hence the answer is <code>2 + 1 + 1 + 1 + 1 = 6</code>.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\" style=\"border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;\">\n<p><strong>Input: </strong> <span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\"> nums = [2,3,3], k = 5 </span></p>\n\n<p><strong>Output: </strong> <span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\"> 4 </span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>There are <code>3</code> subsequences of nums with non-zero power:</p>\n\n<ul>\n\t<li>The subsequence <code>[<u><strong>2</strong></u>,<u><strong>3</strong></u>,<u><strong>3</strong></u>]</code> has 2 subsequences with <code>sum == 5</code>: <code>[<u>2</u>,3,<u>3</u>]</code> and <code>[<u>2</u>,<u>3</u>,3]</code>.</li>\n\t<li>The subsequence <code>[<u><strong>2</strong></u>,3,<u><strong>3</strong></u>]</code> has 1 subsequence with <code>sum == 5</code>: <code>[<u>2</u>,3,<u>3</u>]</code>.</li>\n\t<li>The subsequence <code>[<u><strong>2</strong></u>,<u><strong>3</strong></u>,3]</code> has 1 subsequence with <code>sum == 5</code>: <code>[<u>2</u>,<u>3</u>,3]</code>.</li>\n</ul>\n\n<p>Hence the answer is <code>2 + 1 + 1 = 4</code>.</p>\n</div>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<div class=\"example-block\" style=\"border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;\">\n<p><strong>Input: </strong> <span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\"> nums = [1,2,3], k = 7 </span></p>\n\n<p><strong>Output: </strong> <span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\"> 0 </span></p>\n\n<p><strong>Explanation:&nbsp;</strong>There exists no subsequence with sum <code>7</code>. Hence all subsequences of nums have <code>power = 0</code>.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 100</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>\n\t<li><code>1 &lt;= k &lt;= 100</code></li>\n</ul>\n",
            "translatedTitle": "求出所有子序列的能量和",
            "translatedContent": "<p>给你一个长度为 <code>n</code>&nbsp;的整数数组&nbsp;<code>nums</code>&nbsp;和一个 <strong>正</strong>&nbsp;整数&nbsp;<code>k</code>&nbsp;。</p>\n\n<p>一个整数数组的 <strong>能量</strong>&nbsp;定义为和 <strong>等于</strong>&nbsp;<code>k</code>&nbsp;的子序列的数目。</p>\n\n<p>请你返回 <code>nums</code>&nbsp;中所有子序列的 <strong>能量和</strong>&nbsp;。</p>\n\n<p>由于答案可能很大，请你将它对&nbsp;<code>10<sup>9</sup> + 7</code>&nbsp;<strong>取余</strong>&nbsp;后返回。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\" style=\"border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;\">\n<p><strong>输入：</strong> <span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\"> nums = [1,2,3], k = 3 </span></p>\n\n<p><strong>输出：</strong> <span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\"> 6 </span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>总共有&nbsp;<code>5</code>&nbsp;个能量不为 0 的子序列：</p>\n\n<ul>\n\t<li>子序列&nbsp;<code>[<em><strong>1</strong></em>,<em><strong>2</strong></em>,<em><strong>3</strong></em>]</code> 有&nbsp;<code>2</code>&nbsp;个和为&nbsp;<code>3</code>&nbsp;的子序列：<code>[1,2,<strong><em>3</em></strong>]</code> 和 <code>[<strong><em>1</em></strong>,<strong><em>2</em></strong>,3]</code>&nbsp;。</li>\n\t<li>子序列&nbsp;<code>[<em><strong>1</strong></em>,2,<em><strong>3</strong></em>]</code>&nbsp;有 <code>1</code>&nbsp;个和为&nbsp;<code>3</code>&nbsp;的子序列：<code>[1,2,<strong><em>3</em></strong>]</code>&nbsp;。</li>\n\t<li>子序列&nbsp;<code>[1,<em><strong>2</strong></em>,<em><strong>3</strong></em>]</code> 有&nbsp;<code>1</code>&nbsp;个和为&nbsp;<code>3</code>&nbsp;的子序列：<code>[1,2,<strong><em>3</em></strong>]</code>&nbsp;。</li>\n\t<li>子序列&nbsp;<code>[<em><strong>1</strong></em>,<em><strong>2</strong></em>,3]</code>&nbsp;有&nbsp;<code>1</code>&nbsp;个和为&nbsp;<code>3</code>&nbsp;的子序列：<code>[<strong><em>1</em></strong>,<strong><em>2</em></strong>,3]</code>&nbsp;。</li>\n\t<li>子序列&nbsp;<code>[1,2,<em><strong>3</strong></em>]</code>&nbsp;有&nbsp;<code>1</code>&nbsp;个和为&nbsp;<code>3</code>&nbsp;的子序列：<code>[1,2,<strong><em>3</em></strong>]</code>&nbsp;。</li>\n</ul>\n\n<p>所以答案为&nbsp;<code>2 + 1 + 1 + 1 + 1 = 6</code>&nbsp;。</p>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\" style=\"border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;\">\n<p><strong>输入：</strong> <span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\"> nums = [2,3,3], k = 5 </span></p>\n\n<p><strong>输出：</strong> <span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\"> 4 </span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>总共有&nbsp;<code>3</code>&nbsp;个能量不为 0 的子序列：</p>\n\n<ul>\n\t<li>子序列&nbsp;<code>[<em><strong>2</strong></em>,<em><strong>3</strong></em>,<em><strong>3</strong></em>]</code>&nbsp;有 2 个子序列和为&nbsp;<code>5</code>&nbsp;：<code>[<strong><em>2</em></strong>,3,<strong><em>3</em></strong>]</code> 和&nbsp;<code>[<strong><em>2</em></strong>,<strong><em>3</em></strong>,3]</code>&nbsp;。</li>\n\t<li>子序列&nbsp;<code>[<em><strong>2</strong></em>,3,<em><strong>3</strong></em>]</code>&nbsp;有 1 个子序列和为&nbsp;<code>5</code>&nbsp;：<code>[<strong><em>2</em></strong>,3,<strong><em>3</em></strong>]</code>&nbsp;。</li>\n\t<li>子序列&nbsp;<code>[<em><strong>2</strong></em>,<em><strong>3</strong></em>,3]</code>&nbsp;有 1 个子序列和为 <code>5</code>&nbsp;：<code>[<strong><em>2</em></strong>,<strong><em>3</em></strong>,3]</code>&nbsp;。</li>\n</ul>\n\n<p>所以答案为&nbsp;<code>2 + 1 + 1 = 4</code>&nbsp;。</p>\n</div>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<div class=\"example-block\" style=\"border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;\">\n<p><strong>输入：</strong> <span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\"> nums = [1,2,3], k = 7 </span></p>\n\n<p><strong>输出：</strong> <span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\"> 0 </span></p>\n\n<p><strong>解释：</strong>不存在和为 <code>7</code>&nbsp;的子序列，所以 <code>nums</code>&nbsp;的能量和为&nbsp;<code>0</code>&nbsp;。</p>\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 &lt;= 100</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>\n\t<li><code>1 &lt;= k &lt;= 100</code></li>\n</ul>\n",
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