Problem: A long time ago in some far country lived king Copa. After the recent king's reform, he got so large powers that started to keep the books by himself.

The total income A of his kingdom during 0-th year is known, as well as the total income B during n-th year (these numbers can be negative — it means that there was a loss in the correspondent year). 

King wants to show financial stability. To do this, he needs to find common coefficient X — the coefficient of income growth during one year. This coefficient should satisfy the equation:

A·Xn = B.

Surely, the king is not going to do this job by himself, and demands you to find such number X.

It is necessary to point out that the fractional numbers are not used in kingdom's economy. That's why all input numbers as well as coefficient X must be integers. The number X may be zero or negative.

Input

The input contains three integers A, B, n (|A|, |B| ≤ 1000, 1 ≤ n ≤ 10).

Output

Output the required integer coefficient X, or «No solution», if such a coefficient does not exist or it is fractional. If there are several possible solutions, output any of them.

Examples

Input

2 18 2


Output

3

Input

-1 8 3


Output

-2

Input

0 0 10


Output

5

Input

1 16 5


Output

No solution

Solution (in JAVA):

Solution:


import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class P30A {
    //static long m=1000000007;
    static BigInteger ways(int N,  int K) {
        BigInteger ret = BigInteger.ONE;
        for(int i=N;i>=N-K+1;i--)
        {
             ret = ret.multiply(BigInteger.valueOf(i));
            
        }
        for (int j = 1; j<=K; j++) {
            ret = ret.divide(BigInteger.valueOf(j));
        }
       
            ret=ret.mod(BigInteger.valueOf(1000000007));
        
        return ret;
    }
    public static int prime(int n)
    {
        int f=1;
        if(n==1)
            return 0;
        for(int i=2;i<=(Math.sqrt(n));)
        {
            if(n%i==0)
            {
                f=0;
                break;
            }
            if(i==2)
                i++;
            else
                i+=2;
        }
        if(f==1)
            return 1;
        else 
            return 0;
    }
/*public static long gcd(long x,long y)
{
    if(x%y==0)
        return y;
    else return gcd(y,x%y);
}*/
    public static BigInteger fact(int n)
    {
        BigInteger f=BigInteger.ONE;
        for(int i=1;i<=n;i++)
        {
            f=f.multiply(BigInteger.valueOf(i));
        }
        //f=f.mod(BigInteger.valueOf(m));
        return f;
    }
public static int gcd(int x,int y)
{
    if(x%y==0)
        return y;
    else return gcd(y,x%y);
}
public static int max(int a,int b)
{
    if(a>b)
        return a;
    else
        return b;
}
public static int min(int a,int b)
{
    if(a>b)
        return b;
    else 
        return a;
}
    public static void main(String[] args) throws Exception{
        
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringBuilder sb=new StringBuilder("");
        //int t=Integer.parseInt(br.readLine());
    //  while(t-->0)
        //{
        //int n=Integer.parseInt(br.readLine());
        //String l[]=br.readLine().split(" ");
        //long n=Long.parseLong(br.readLine());
        //l=br.readLine().split(" ");
    //  int m=Integer.parseInt(l[0]);
        //long m=Long.parseLong(l[0]);
        //char ch=a.charAt();
    //  char c[]=new char[n];
        //int a[]=new int[n];
        /*for(int i=0;i<n;i++)
        {
            
        }*/
        //int a[][]=new int[n][n];
        //HashMap<Integer,Integer>hm=new HashMap<Integer,Integer>();
        //HashMap<Integer,String>hm=new HashMap<Integer,String>();
        //HashMap<Integer,Long>hm=new HashMap<Integer,Long>();
        //hm.put(1,1);
        //HashSet<Integer>hs=new HashSet<Integer>();
        //HashSet<Long>hs=new HashSet<Long>();
        //HashSet<String>hs=new HashSet<String>();
        //hs.add(x);
        //Stack<Integer>s=new Stack<Integer>();
        //s.push(x);
        //s.pop(x);
        //Queue<Integer>q=new LinkedList<Integer>();
        //q.add(x);
        //q.remove(x);
        //long a[]=new long[n];
        //long x=Long.parseLong(l[0]);
        //for(int i=0;i<n;i++)
        //{
            //a[i]=Long.parseLong(l[i]);
        //}
        //int min=100000000;
    //  String a=br.readLine();
        //for(int i=0;i<n;i++)
        //{
            //a[i]=Integer.parseInt(l[i]);
        //}
        // char a[]=c.toCharArray();
        //char ch=l[0].charAt(0);
        //long c1=(long)Math.ceil(n/(double)a);
        //Arrays.sort(a);
          // int f1[]=new int[26];
           //int f2[]=new int[26];
        //for(int i=0;i<n;i++)
        //{
        //int x=a.charAt(0);
            //f1[x-97]++;
        //}
        /*for(int i=0;i<n;i++)
        {
            for(int j=0;j<n;j++)
            {
                
            }
        }*/
        
      String l[]=br.readLine().split(" ");
      int a=Integer.parseInt(l[0]);
      int b=Integer.parseInt(l[1]);
      int n=Integer.parseInt(l[2]);
      int x=0;
      int c=0;
      if(a!=0&&b!=0)
      {
        
          int p=(int)Math.abs(a);
          int q=(int)Math.abs(b);
          if(q%p==0&&q>=p)
          {
              int y=b/a;
              if(y>0)
              {
                  int s=(int)Math.ceil(Math.pow(y, 1.0/(double)n));
                 // int t=(int)Math.pow(y,(double) 1.0/(double)n);
                  double d=Math.pow(y, (double)1.0/(double)n);
                  d = Math.round(d*1000000.0)/1000000.0;
                  int t=(int)d;
                 // System.out.println(s+" "+d);
                  if(s==t)
                  {
                      x=s;
                      c=1;
                  }
              }
              else
              {
                  y=(int)Math.abs(y);
                  int s=(int)Math.ceil(Math.pow(y, 1.0/n));
                  int t=(int)Math.pow(y, 1.0/n);
                  if(s==t)
                  {
                      x=s;
                      c=1;
                      x=x*(-1);
                  }
              }
          }
      }
      if(a==0&&b!=0)
      {
          c=0;
      }
      if(a!=0&&b==0)
      {
          c=1;
          x=0;
      }
      if(a==0&&b==0)
      {
         c=1;
          x=1;
      }
      if(c==0)
             System.out.println("No solution");
      else
          System.out.println(x);
        
        //}
    }
}