You are given an integer array nums and an integer k.

In one operation, you perform the following actions:

• Select the two smallest integers x and y from nums.

• Remove x and y from nums.

• Add $\min(x, y) imes 2 + \max(x, y)$ to nums.

Return the minimum number of operations required so that every element in nums is greater than or equal to k.

Constraints:

• $2 \leq$ nums.length $\leq 2 \cdot 10^5$

• $1 \leq$ nums[i] $\leq 10^9$

• $1 \leq$ k $\leq 10^9$

• The input is generated such that an answer always exists, meaning that all elements in nums will eventually be greater than or equal to k after performing some number of operations.

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.