You are given an integer array nums of length n and a positive integer k.

The power of an array is defined as the number of its subsequences whose elements sum up to k.

Return the sum of the power of all subsequences of nums. Since the answer may be very large, return it modulo $10^9 + 7$.

Constraints:

• $1 \leq$ n $\leq 100$

• $1 \leq$ nums[i] $\leq 10^4$

• $1 \leq$ k $\leq 100$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.