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:
i0, i1, ... ,ik be the indices of the heroes in a group. Then, the power of this group is max(nums[i0], nums[i1], ... ,nums[ik])2 * min(nums[i0], nums[i1], ... ,nums[ik]).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.
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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. \n7th 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
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Constraints:
\n\n1 <= nums.length <= 1051 <= nums[i] <= 109Compiled with clang 11 using the latest C++ 20 standard.
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