Sort by sum of digits

The sum of a number’s digits is associated with some of its properties. In particular, it is easy to determine divisibility by $3$ and $9$ using the sum of digits. Computer scientists from Bergen decided to investigate natural numbers and the sums of their digits.

It is well known that working with sorted data is easier than with unsorted data. Therefore, the researchers decided to sort natural numbers by the sum of their digits. If several numbers have equal sums of digits, these numbers are arranged in ascending order.

When the scientists sorted the numbers from $1$ to $20$, they obtained the sequence: $1$, $10$, $2$, $11$, $20$, $3$, $12$, $4$, $13$, $5$, $14$, $6$, $15$, $7$, $16$, $8$, $17$, $9$, $18$, $19$.

For a small quantity of numbers, the sorting was performed quickly. When the research expanded to a wider range, some difficulties arose. One of them was to find the position of the number $K$ in the sorted sequence of the first $N$ natural numbers. Your task is to solve this problem.

Write a program to calculate the position of $K$ in the sorted sequence of the first $N$ natural numbers.