!
You are one of ICPC participants and in charge of developing a library for multiprecision numbers and radix conversion. You have just finished writing the code, so next you have to test if it works correctly. You decided to write a simple, well-known factorial function for this purpose:
M! = i = M × (M − 1) × ··· × 2 × 1, 0! = 1.
Your task is to write a program that shows the number of trailing zeros when you compute M! in base N, given N andM.
Input
The input contains multiple data sets. Each data set is described by one line in the format below:
N M
where N is a decimal number between 8 and 36 inclusive, and M is given in the string representation in base N. Exactly one white space character appears between them. The string representation of M contains up to 12 characters in base N. In case N is greater than 10, capital letters A, B, C, ... may appear in the string representation, and they represent 10,11, 12, ..., respectively.
The input is terminated by a line containing two zeros. You should not process this line.
Output
For each data set, output a line containing a decimal integer, which is equal to the number of trailing zeros in the string representation of M! in base N.