#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<cassert>
#include<iostream>
#include<sstream>
#include<string>
#include<vector>
#include<queue>
#include<set>
#include<map>
#include<utility>
#include<numeric>
#include<algorithm>
#include<bitset>
#include<complex>
#include<stack>

using namespace std;

typedef long long Int;
typedef vector<int> vint;
typedef pair<int,int> pint;
typedef vector<string> vstring;
typedef vector<pint> vpint;
typedef stringstream SS;

#ifdef DEBUG
#define debug cout
#else
SS ss;
#define debug ss
#endif

template<class T> void chmin(T &t, T f) { if (t > f) t = f; }
template<class T> void chmax(T &t, T f) { if (t < f) t = f; }
int in() { int x; scanf("%d", &x); return x; }

#define rep(i,n) for(int i=0;i<(n);++i)
#define repn(i,m,n) for(int i=(m);i<(n);++i)
#define repd(i,n) for(int i=(n)-1;i>=0;--i)
#define repnd(i,m,n) for(int i=(n)-1;i>=(m);--i)
#define rep0(i,n) for(i=0;i<(n);++i)
#define repn0(i,m,n) for(i=(m);i<(n);++i)
#define repd0(i,n) for(i=(n)-1;i>=0;--i)
#define repnd0(i,m,n) for(i=(n)-1;i>=(m);--i)
#define repc(i,n) for(int i=0;i<=(n);++i)
#define repcn(i,m,n) for(int i=(m);i<=(n);++i)
#define repcd(i,n) for(int i=(n);i>=0;--i)
#define repcnd(i,m,n) for(int i=(n);i>=(m);--i)
#define repc0(i,n) for(i=0;i<=(n);++i)
#define repcn0(i,m,n) for(i=(m);i<=(n);++i)
#define repcd0(i,n) for(i=(n);i>=0;--i)
#define repcnd0(i,m,n) for(i=(n);i>=(m);--i)
#define all(n) n.begin(),n.end()
#define sz(n) ((int)(n).size())
#define IL for(;;)
#define MP make_pair
#define PB push_back
#define X second
#define Y first
#define p_queue(n) priority_queue<n,vector<n>,greater<n> >
#define PUTLINE debug<<"LINE:"<<__LINE__<<endl;

const Int INF = 4000000000000000000LL;
const double EPS = 1e-10;
const double PI = acos(-1.0);

const int dx[]={1,-1,0,0,1,1,-1,-1,0};
const int dy[]={0,0,1,-1,1,-1,1,-1,0};

Int dig(char c){
	if(isdigit(c))return c-'0';
	return c-'A'+10;
}

int main() {
	Int n,m,nn,mm,res,r;
	vector<pair<Int,Int> > p;
	string str;
	IL{
		cin>>n>>str;
		if(n==0)break;
		m=0;
		rep(i,sz(str)){
			m=m*n+dig(str[i]);
		}
		nn=n;
		p.clear();
		for(Int i=2;nn!=1;++i){
			if(nn%i==0){
				Int count=0;
				while(nn%i==0){
					++count;
					nn/=i;
				}
				p.PB(MP(i,count));
			}
		}
		res=INF;
		rep(j,sz(p)){
			mm=m;
			r=0;
			while(mm>0){
				mm/=p[j].first;
				r+=mm;
			}
			chmin(res,r/p[j].second);
		}
		cout<<res<<endl;
	}
	return 0;
}
### Prompt

Please create a solution in cpp to the following problem:

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:

<image>

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.

Example

Input

10 500
16 A
0 0


Output

124
2

### Response

```cpp
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<cassert>
#include<iostream>
#include<sstream>
#include<string>
#include<vector>
#include<queue>
#include<set>
#include<map>
#include<utility>
#include<numeric>
#include<algorithm>
#include<bitset>
#include<complex>
#include<stack>

using namespace std;

typedef long long Int;
typedef vector<int> vint;
typedef pair<int,int> pint;
typedef vector<string> vstring;
typedef vector<pint> vpint;
typedef stringstream SS;

#ifdef DEBUG
#define debug cout
#else
SS ss;
#define debug ss
#endif

template<class T> void chmin(T &t, T f) { if (t > f) t = f; }
template<class T> void chmax(T &t, T f) { if (t < f) t = f; }
int in() { int x; scanf("%d", &x); return x; }

#define rep(i,n) for(int i=0;i<(n);++i)
#define repn(i,m,n) for(int i=(m);i<(n);++i)
#define repd(i,n) for(int i=(n)-1;i>=0;--i)
#define repnd(i,m,n) for(int i=(n)-1;i>=(m);--i)
#define rep0(i,n) for(i=0;i<(n);++i)
#define repn0(i,m,n) for(i=(m);i<(n);++i)
#define repd0(i,n) for(i=(n)-1;i>=0;--i)
#define repnd0(i,m,n) for(i=(n)-1;i>=(m);--i)
#define repc(i,n) for(int i=0;i<=(n);++i)
#define repcn(i,m,n) for(int i=(m);i<=(n);++i)
#define repcd(i,n) for(int i=(n);i>=0;--i)
#define repcnd(i,m,n) for(int i=(n);i>=(m);--i)
#define repc0(i,n) for(i=0;i<=(n);++i)
#define repcn0(i,m,n) for(i=(m);i<=(n);++i)
#define repcd0(i,n) for(i=(n);i>=0;--i)
#define repcnd0(i,m,n) for(i=(n);i>=(m);--i)
#define all(n) n.begin(),n.end()
#define sz(n) ((int)(n).size())
#define IL for(;;)
#define MP make_pair
#define PB push_back
#define X second
#define Y first
#define p_queue(n) priority_queue<n,vector<n>,greater<n> >
#define PUTLINE debug<<"LINE:"<<__LINE__<<endl;

const Int INF = 4000000000000000000LL;
const double EPS = 1e-10;
const double PI = acos(-1.0);

const int dx[]={1,-1,0,0,1,1,-1,-1,0};
const int dy[]={0,0,1,-1,1,-1,1,-1,0};

Int dig(char c){
	if(isdigit(c))return c-'0';
	return c-'A'+10;
}

int main() {
	Int n,m,nn,mm,res,r;
	vector<pair<Int,Int> > p;
	string str;
	IL{
		cin>>n>>str;
		if(n==0)break;
		m=0;
		rep(i,sz(str)){
			m=m*n+dig(str[i]);
		}
		nn=n;
		p.clear();
		for(Int i=2;nn!=1;++i){
			if(nn%i==0){
				Int count=0;
				while(nn%i==0){
					++count;
					nn/=i;
				}
				p.PB(MP(i,count));
			}
		}
		res=INF;
		rep(j,sz(p)){
			mm=m;
			r=0;
			while(mm>0){
				mm/=p[j].first;
				r+=mm;
			}
			chmin(res,r/p[j].second);
		}
		cout<<res<<endl;
	}
	return 0;
}
```