Time Limit : 8 sec, Memory Limit : 131072 KB

Problem C: !

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:

Your task is to write a program that shows the number of trailing zeros when you compute M! in base N, given N and M.


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 repre- sentation 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.


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.

Sample Input

10 500
16 A
0 0

Output for the Sample Input


Source: ACM-ICPC Japan Alumni Group Summer Camp 2007 , Day 2, Tokyo, Japan, 2007-09-23