Wavy numbers

题意翻译

### 题目描述 我们将一类正整数称为“波浪数”，它的每个数位上的数都大于或小于两边数位上的数。例如，$35270$，$102$，$747$，$20$ 和 $3$ 都是波浪数；而 $123$，$1000$ 和 $2212$ 不是波浪数。 你的任务是找到第 $k$ 小且能被 $n$ 整除的波浪数 $r$。 保证 $r \le 10^{14}$。 ### 输入格式 输入仅有一行，包含两个整数 $n$ 和 $k$（$1 \le n,k \le 10^{14}$） 。 ### 输出格式 输出问题的答案 $r$，如果答案不存在或大于 $10^{14}$，则输出`-1`。 ### 说明/提示 第一个样例中，前四个能被 $n$ 整除的波浪数为：$492$，$615$，$738$ 和 $1845$。

题目描述

A wavy number is such positive integer that for any digit of its decimal representation except for the first one and the last one following condition holds: the digit is either strictly larger than both its adjacent digits or strictly less than both its adjacent digits. For example, numbers $ 35270 $ , $ 102 $ , $ 747 $ , $ 20 $ and $ 3 $ are wavy and numbers $ 123 $ , $ 1000 $ and $ 2212 $ are not. The task is to find the $ k $ -th smallest wavy number $ r $ that is divisible by $ n $ for the given integer values $ n $ and $ k $ . You are to write a program that will find the value of $ r $ if it doesn't exceed $ 10^{14} $ .

输入输出格式

输入格式

The only line of input contains two integers $ n $ and $ k $ , separated by a single space ( $ 1<=n,k<=10^{14} $ ).

输出格式

Your task is to output the only integer $ r $ — the answer to the given problem. If such number does not exist or it is larger than $ 10^{14} $ , then print "-1" (minus one without the quotes) instead.

输入输出样例

输入样例 #1

123 4

输出样例 #1

1845

输入样例 #2

100 1

输出样例 #2

-1

输入样例 #3

97461 457

输出样例 #3

1805270103

说明

The values of the first four wavy numbers that are divisible by $ n $ for the first sample are: $ 492 $ , $ 615 $ , $ 738 $ and $ 1845 $ .