You are given an integer array nums consisting of powers of $2$, and an integer target.

In a single operation, you can select any element nums[i] such that nums[i] $> 1$, remove it from nums, and add two occurrences of nums[i] $/ 2$ to nums.

Return the minimum number of operations required to make nums contain a subsequence whose sum is equal to target. If no such subsequence can be formed, return $-1$.

Note: A subsequence is an array obtained by deleting zero or more elements from another array without altering the relative order of the remaining elements.

Constraints:

• $1 \leq$ nums.length $\leq 1000$

• $1 \leq$ nums[i] $\leq 2^{30}$

• nums consists only of powers of $2$ with non negative exponents.

• $1 \leq$ target $< 2^{31}$

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.