A number where one digit is the sum of the other digits is called a digit sum number or DS-number for short. For example, 352, 3003 and 32812 are DS-numbers.

We define S(n) to be the sum of all DS-numbers of n digits or less.

You are given S(3) = 63270 and S(7) = 85499991450.

Find S(2020). Give your answer modulo 10^{16} .