{ "data": { "question": { "questionId": "2784", "questionFrontendId": "2681", "categoryTitle": "Algorithms", "boundTopicId": 2266665, "title": "Power of Heroes", "titleSlug": "power-of-heroes", "content": "

You are given a 0-indexed integer array nums representing the strength of some heroes. The power of a group of heroes is defined as follows:

\n\n\n\n

Return the sum of the power of all non-empty groups of heroes possible. Since the sum could be very large, return it modulo 109 + 7.

\n\n

 

\n

Example 1:

\n\n
\nInput: nums = [2,1,4]\nOutput: 141\nExplanation: \n1st group: [2] has power = 22 * 2 = 8.\n2nd group: [1] has power = 12 * 1 = 1. \n3rd group: [4] has power = 42 * 4 = 64. \n4th group: [2,1] has power = 22 * 1 = 4. \n5th group: [2,4] has power = 42 * 2 = 32. \n6th group: [1,4] has power = 42 * 1 = 16. \n​​​​​​​7th group: [2,1,4] has power = 42​​​​​​​ * 1 = 16. \nThe sum of powers of all groups is 8 + 1 + 64 + 4 + 32 + 16 + 16 = 141.\n\n
\n\n

Example 2:

\n\n
\nInput: nums = [1,1,1]\nOutput: 7\nExplanation: A total of 7 groups are possible, and the power of each group will be 1. Therefore, the sum of the powers of all groups is 7.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "英雄的力量", "translatedContent": "

给你一个下标从 0 开始的整数数组 nums ，它表示英雄的能力值。如果我们选出一部分英雄，这组英雄的 力量 定义为：

\n\n\n\n

请你返回所有可能的 非空 英雄组的 力量 之和。由于答案可能非常大，请你将结果对 109 + 7 取余。

\n\n

 

\n\n

示例 1：

\n\n
\n输入：nums = [2,1,4]\n输出：141\n解释：\n第 1 组：[2] 的力量为 22 * 2 = 8 。\n第 2 组：[1] 的力量为 12 * 1 = 1 。\n第 3 组：[4] 的力量为 42 * 4 = 64 。\n第 4 组：[2,1] 的力量为 22 * 1 = 4 。\n第 5 组：[2,4] 的力量为 42 * 2 = 32 。\n第 6 组：[1,4] 的力量为 42 * 1 = 16 。\n第​ ​​​​​​7 组：[2,1,4] 的力量为 42​​​​​​​ * 1 = 16 。\n所有英雄组的力量之和为 8 + 1 + 64 + 4 + 32 + 16 + 16 = 141 。\n
\n\n

示例 2：

\n\n
\n输入：nums = [1,1,1]\n输出：7\n解释：总共有 7 个英雄组，每一组的力量都是 1 。所以所有英雄组的力量之和为 7 。\n
\n\n

 

\n\n

提示：

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