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