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ZOJ Problem Set - 2599
Graduated Lexicographical Ordering

Time Limit: 10 Seconds      Memory Limit: 32768 KB

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.

  • 120 < grlex4 since w(120) = 1 + 2 + 0 = 3 < 4 = w(4).
  • 555 < grlex78 since w(555) = 15 = w(78) and "555" is lexicographicaly smaller than "78".
  • 20 < grlex200 since w(20) = 2 = w(200) and "20" is lexicographicaly smaller than "200".

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.


Input

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.


Output

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.


Sample Input

20 10
0 0

Sample Output

2 14


Author: Andrew Stankevich
Source: Andrew Stankevich's Contest #6
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