Wavy numbers

1000ms

262144K

Description:

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 10¹⁴.

Input:

The only line of input contains two integers n and k, separated by a single space (1 ≤ n, k ≤ 10¹⁴).

Output:

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 10¹⁴, then print "-1" (minus one without the quotes) instead.

Sample Input:

123 4

Sample Output:

Sample Input:

100 1

Sample Output:

-1

Sample Input:

97461 457

Sample Output:

1805270103

Note:

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

Informação

Provedor Codeforces

Código CF478E