You are given two integers num and sum.

A positive integer is defined as good if:

• It contains exactly num digits without leading zeros.

• The sum of its digits equals sum.

The score of a good integer is the sum of the squares of its digits.

Return the good integer that achieves the maximum score as a string. If there are multiple good integers that achieve the maximum score, return the largest one among them. If no good integer exists, return an empty string "".

Constraints:

• $1 \leq$ num $\leq 2 imes 10^5$

• $1 \leq$ sum $\leq 2 imes 10^6$

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.