A. Accounting

A. Accounting

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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.

Sample test(s)

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

/* ***********************************************
Author        :
Created Time  :2015/6/14 9:23:25
File Name     :7.cpp
************************************************ */
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <stdio.h>
#include <algorithm>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <string>
#include <math.h>
#include <stdlib.h>
#include <iomanip>
#include <list>
#include <deque>
#include <stack>
#define ull unsigned long long
#define ll long long
#define mod 90001
#define INF 1<<30
#define maxn 10000+10
#define cle(a) memset(a,0,sizeof(a))
const ull inf = 1LL << 61;
const double eps=1e-5;
using namespace std;

bool cmp(int a,int b){
    return a>b;
}
int poww(int a,int b){
int t=1;
for(int i=1;i<=b;i++){
t*=a;
}
return t;
}
int main()
{
    #ifndef ONLINE_JUDGE
    //freopen("in.txt","r",stdin);
    #endif
    //freopen("out.txt","w",stdout);
int n,a,b;
while(cin>>a>>b>>n){
if(a==0&&b==0){
cout<<1<<endl;
continue;
}
if(a==0){
 puts("No solution");continue;
}
if((b%a)!=0){
 puts("No solution");continue;
}
int c=b/a;
int mark=0;
int ans;
if(c>=0)
for(int i=0;i<=c;i++){
if(c==poww(i,n)){
mark=1;
ans=i;
break;
}
}
else for(int i=c;i<=0;i++){
if(c==poww(i,n)){
ans=i;
mark=1;break;
}
}
if(mark)cout<<ans<<endl;
else puts("No solution");
}
    return 0;
}