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.*;
public class code {
	static PrintWriter pw;
	static boolean[] visit;
	static ArrayList<Pair>[] adj;
	static ArrayList<Integer> list;
	static long max=01;
	static void dfs(int i, long c) {
		visit[i]=true;
		max=Math.max(c, max);
		for(Pair p: adj[i]) {
			if(!visit[p.x-1]) {
				dfs(p.x-1, c+1l*p.y);
			}
		}
	}
	public static double dist(Pair a, Pair b) {
		return Math.sqrt((a.x-b.x)*(a.x-b.x)+ (a.y-b.y)*(a.y-b.y));
	}
	static boolean belong(long x, int div) {
		if(x>=1900) {
			return div==1;
		}else {
			return div==2;
		}
	}
	static int test(Pair[] arr, long mid) {
		for(int i=arr.length-1; i>=0; i--) {
			if(belong(mid-arr[i].x, arr[i].y)) {
				mid-=arr[i].x;
			}else {
				if(arr[i].y==1) {
					return -1;
				}else {
					return 1;
				}
			}
		}
		return 0;
	}
	static boolean pf(int n) {
		return Math.abs(Math.sqrt(n)*Math.sqrt(n)-n)<=1e-8;
	}
	static boolean sign(int n) {
		return n>0;
	}
	public static void main(String[] args) throws Exception {
		Scanner sc= new Scanner(System.in);
		pw = new PrintWriter(System.out);
		int a=sc.nextInt(),b=sc.nextInt();
		if(a==0) {
			if(b==0) {
				pw.println(1);
				pw.flush();
				return;
			}else {
				pw.println("No solution");
				pw.flush();
				return;
			}
		}
		boolean valid=b%a==0;
		double n=sc.nextDouble();
		double ans=Math.pow(Math.abs(b/a), 1/n);
		valid=valid?(ans%1<=1e-9 || ans%1>=1-1e-9):valid;
		if(valid) {
			ans=ans%1>0.5? (int)ans+1:(int)ans;
			if(sign(a)!=sign(b))
				ans*=-1;
			pw.println((int)ans);
		}else {
			pw.println("No solution");
		}
		pw.close();
	}
	static class Scanner {
		StringTokenizer st;
		BufferedReader br;
 
		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}
 
		public Scanner(FileReader r) {
			br = new BufferedReader(r);
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
 
		public int[] nextArr(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < arr.length; i++)
				arr[i] = nextInt();
			return arr;
		}
		public Integer[] nextsort(int n) throws IOException{
			Integer[] arr=new Integer[n];
			for(int i=0; i<n; i++) 
				arr[i]=nextInt();
			return arr;
		}
		public boolean ready() throws IOException {
			return br.ready();
		}
	}
	static class Pair implements Comparable<Pair>{
		int x;
		int y;
		public Pair(int a, int b) {
			this.x=a;
			this.y=b;
		}
		public int compareTo(Pair other) {
			return this.y-other.y;
		}
	}
	static class Triple implements Comparable<Triple>{
		int x;
		int y;
		boolean d;
		public Triple(int a, int b, boolean t) {
			this.x=a;
			this.y=b;
			this.d=t;
		}
		public int compareTo(Triple other) {
			if(this.d && !other.d) {
				return 1;
			}else if(!this.d && other.d) {
				return -1;
			}else {
				return this.y-other.y;
			}
		}
	}
}