Problem:
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.

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 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.

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.

Sample Input

10 500
16 A
0 0

Output for the Sample Input

124
2

Solution in Ruby (judge verdict: Accepted)

#!/usr/bin/ruby
require 'mathn'
h={};2.step(36){|i|h[i]=i.prime_division}
while(l=gets.chomp)!="0 0"
	l=l.split
	n=l[0].to_i;m=l[1].to_i(n)
	p h[n].map{|a,b|
		z=m;r=0
		while z>0 do r+=(z=z.div(a)) end
		r.div(b)
	}.min
end