46 - Andrew Stankevich's Contest, Warmup - 1005
Consider integer numbers from 1 to n. Let us call the sum of digits of an integer number its weight. Denote the weight of the number x as w(x).
Now let us order the numbers using so called graduated lexicographical ordering, or shorter grlex ordering. Consider two integer numbers a and b. If w(a) < w(b) then a goes before b in grlex ordering. If w(a) = w(b) then a goes before b in grlex ordering if and only if the decimal representation of a is lexicographically smaller than the decimal representation of b.
Let us consider some examples.
Given n and some integer number k, find the position of the number k in grlex ordering of integer numbers from 1 to n, and the k-th number in this ordering.
There are several lines in the input file, and each line stands two integers n and k (1 <= k <= n <= 1018). A line with n = k = 0 ends up the input.
For each line in the input, output one line in the output file. First print the position of the number k in grlex ordering of integer numbers from 1 to n, and then the integer that occupies the k-th position in this ordering.
20 10 0 0
Author: Andrew Stankevich