This approach involves sorting the array and then using a two pointers method to determine valid subsequences. We focus on the potential minimum and maximum values in a subsequence.

After sorting, use two pointers, one starting from the beginning of the array (for the minimum) and the other from the end (for the maximum). For each minimum, the number of valid subsequences is determined by how many elements from the minimum can pair with elements from the maximum such that their sum is less than or equal to the target. The number of subsequences can be calculated using the binary exponentiation of 2 with the distance between the two pointers.

This approach involves dynamic programming where pre-computed powers of 2 are used to calculate valid subsequences. Using arrays to store results dynamically avoids repetitive calculations and exploits binary indexing for faster computation on potential subsets.

The idea is to create a precompute power array of size n to store power values of 2 up to n. Iterating with this precompute allows identifying valid subsequences without recalculating powers each iteration, enhancing efficiency especially for extremely large arrays.