#2113. Zju2599 Graduated Lexicographical Ordering

题目描述

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.

考虑所有从1到n的整数。我们设一个整数 x 的十进制各位数字之和为 w(x)。
让我们重新将整数排序：对于整数a 和整数b，如果w(a)<w(b)，则a 在 b之前。如果
w(a)=w(b)，那么a 在b之前当且仅当a 的十进制表示在字典序中小于 b 的十进制表示。例
如：
120 < grlex4 因为 w(120) = 1 + 2 + 0 = 3 < 4 = w(4)。
555 < grlex78 因为 w(555) = 15 = w(78) 并且 "555" 的字典序小于 "78"。
20 < grlex200 因为 w(20) = 2 = w(200) 并且 "20" 的字典序小于 "200"。
给定整数n和k，你需要求出1-n中的数按照上述方法排序后，k是第几个数，以及第 k
个数是多少。
输入：包含多组数据，每组数据包含两个整数 n和 k。输入的最后一行是 n=k=0。
输出：对于每组数据，输出一行两个整数，分别表示k在 1-n中的编号，以及第 k个数
是多少。
数据规模：1 ≤ k ≤ n ≤ 10^18
。

输入格式

There are several lines in the input file, and each line stands two integers n and k (1 <= k <= n <= 10^18).

输出格式

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.

样例

样例输入

20 10  

样例输出

2 14  

数据范围与提示