Number of Subsequences That Satisfy the Given Sum Condition
You receive an array of integers nums and an integer target.
Find and provide the count of non-empty subsequences of nums such that the sum of the fewest and largest element on it is less or equal to target. Since the answer may be too large, provide it modulo 10^9+ 7.
Input: nums = [3,5,6,7], target = 9
Output: 4
Explanation: There are 4 subsequences that satisfy the condition.
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[3] -> Min value + max value <= target (3 + 3 <= 9)
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[3,5] -> (3 + 5 <= 9)
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[3,5,6] -> (3 + 6 <= 9)
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[3,6] -> (3 + 6 <= 9)
Input: nums = [3,3,6,8], target = 10
Output: 6
Explanation: There are 6 subsequences that satisfy the condition. (nums can have repeated numbers).
[3], [3], [3,3], [3,6], [3,6], [3,3,6]
Input: nums = [2,3,3,4,6,7], target = 12
Output: 61
Explanation: There are 63 non-empty subsequences, two of them do not satisfy the condition ([6,7], [7]).
Number of valid subsequences (63 - 2 = 61).
Constraints
1 <= nums.length <= 10^51 <= nums[i] <= 10^61 <= target <= 10^6
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