3723 - Maximize Sum of Squares of Digits.

Medium

You are given two positive integers num and sum.

A positive integer n is good if it satisfies both of the following:

• The number of digits in n is exactly num.

• The sum of digits in n is exactly sum.

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

Return a string denoting the good integer n that achieves the maximum score. If there are multiple possible integers, return the maximum one. If no such integer exists, return an empty string.

Example 1:

Input: num = 2, sum = 3

Output: "30"

Explanation:

There are 3 good integers: 12, 21, and 30.

• The score of 12 is <code>1² + 2² = 5</code>.

• The score of 21 is <code>2² + 1² = 5</code>.

• The score of 30 is <code>3² + 0² = 9</code>.

The maximum score is 9, which is achieved by the good integer 30. Therefore, the answer is "30".

Example 2:

Input: num = 2, sum = 17

Output: "98"

Explanation:

There are 2 good integers: 89 and 98.

• The score of 89 is <code>8² + 9² = 145</code>.

• The score of 98 is <code>9² + 8² = 145</code>.

The maximum score is 145. The maximum good integer that achieves this score is 98. Therefore, the answer is "98".

Example 3:

Input: num = 1, sum = 10

Output: ""

Explanation:

There are no integers that have exactly 1 digit and whose digits sum to 10. Therefore, the answer is "".

Constraints:

• <code>1 <= num <= 2 * 10⁵</code>

• <code>1 <= sum <= 2 * 10⁶</code>