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Sum of Good Subsequences

You are given an integer array nums.

You are given an integer array nums. A good subsequence is defined as a subsequence of nums where the absolute difference between any two consecutive elements in the subsequence is exactly 1.

Return the sum of all possible good subsequences of nums.

Since the answer may be very large, return it modulo 10^9 + 7.

Note that a subsequence of size 1 is considered good by definition.

Sum of Good Subsequences diagram

Example 1

Input: nums = [1,2,1]

Output: 14

Example 2

Input: nums = [3,4,5]

Output: 40

Constraints

  • 1 <= nums.length <= 10^5
  • 0 <= nums[i] <= 10^5

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