# Poj Solution 1707

```http://poj.org/problem?id=1707

//* @author: ccQ.SuperSupper
import java.io.*;
import java.util.*;
import java.math.*;
import java.text.*;
public class Main
{
static class com
{
BigInteger a,b;//a/b...
{
com ret=new com();
BigInteger lcm;
lcm=b.multiply(C.b).divide(b.gcd(C.b));
ret.b=lcm;
lcm=ret.b.gcd(ret.a);
ret.a=ret.a.divide(lcm);
ret.b=ret.b.divide(lcm);
return ret;
}
com sub(com C)
{
com ret=new com();
BigInteger lcm;
lcm=b.multiply(C.b).divide(b.gcd(C.b));
ret.b=lcm;
ret.a=a.multiply(lcm.divide(b)).subtract((C.a.multiply(lcm.divide(C.b))));
lcm=ret.b.gcd(ret.a);
ret.a=ret.a.divide(lcm);
ret.b=ret.b.divide(lcm);
return ret;
}
void show()
{
System.out.println(a+" / "+b);
}
}

static BigInteger s[][]=new BigInteger[105][105],fac[]=new BigInteger[105],dp[][]=new BigInteger[105][105];
static com B[]=new com[105];
static com buf[] = new com[105];
static void mkstri()
{
int i,j;
com tmp = new com();
for (i = 0; i < 105; ++i) B[i] = new com();
for(i=1;i< 105;++i)
{
dp[i][0]=dp[i][i]=BigInteger.ONE;
for(j=1;j< i;++j)
}
for(i=1;i< 105;++i)
s[i][i]=s[i][1]=BigInteger.ONE;
for(i=2;i< 105;++i)
for(j=2;j< i;++j)
fac[0]=BigInteger.ONE;
for(i=1;i< 105;++i)
fac[i]=fac[i-1].multiply(BigInteger.valueOf(i));
B[0].a=B[0].b=BigInteger.ONE;
for(i=1;i< 105;++i)
{
B[i].a=BigInteger.ZERO;
B[i].b=BigInteger.ONE;
for(j=1;j<=i;++j)
{
tmp.a=fac[j].multiply(s[i][j]);
tmp.b=BigInteger.valueOf(j+1);
if((i+j)%2==0)
else
B[i]=B[i].sub(tmp);
}
}
}

public static void main(String args[]) throws Exception {
Scanner cin=new Scanner(System.in);
mkstri();
BigInteger ans,tmp,G;
int k,i;
for(i=0;i< 105;++i)buf[i]=new com();
while(cin.hasNext())
{
k=cin.nextInt();
//k+1...
ans=BigInteger.ONE;
for(i=0;i<=k;++i)
{
buf[i].b=B[i].b.multiply(BigInteger.valueOf(k+1));
buf[i].a=B[i].a.multiply(dp[k+1][i]);
G=buf[i].a.gcd(buf[i].b);
buf[i].a=buf[i].a.divide(G);
buf[i].b=buf[i].b.divide(G);
ans=ans.multiply(buf[i].b).divide(buf[i].b.gcd(ans));
}
System.out.print(ans);
for(i=0;i<=k;++i)
{
G=ans.divide(buf[i].b);
System.out.print(" "+buf[i].a.multiply(G));
}
System.out.println(" 0");
}
}
}
```
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