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.BufferedReader;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;

/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */
/**
 *
 * @author Trung Pham
 */
public class A {

    public static void main(String[] args) throws FileNotFoundException, IOException {
        Scanner in = new Scanner();
        PrintWriter out = new PrintWriter(System.out);
        int A = in.nextInt();
        int B = in.nextInt();
        int n = in.nextInt();
        if (A == 0) {
            if (B != 0) {
                out.println("No solution");
            } else {
                out.println(5);
            }
        } else if (B % A != 0) {
            out.println("No solution");
        } else {
            int val = B / A;
            boolean neg = false;
            if (val < 0 && n % 2 != 0) {
                val = -val;
                neg = true;
            }
            int X = (int) Math.ceil(Math.pow(val, (double) 1 / n));
           // System.out.println(X);
            if (Math.pow(X, n) == val) {
                if (neg && n % 2 != 0) {
                    out.println(-X);
                } else {
                    out.println(X);
                }
//            } else if (Math.pow(X + 1, n) == val) {
//                if (neg && n % 2 != 0) {
//                    out.println(-(X + 1));
//                } else {
//                    out.println(X + 1);
//                }
//            } else if (Math.pow(X - 1, n) == val) {
//                if (neg && n % 2 != 0) {
//                    out.println(-(X - 1));
//                } else {
//                    out.println(X - 1);
//                }
            } else {
                out.println("No solution");
            }
        }

        out.close();
    }

    public static int dist(int x0, int y0, int x1, int y1) {
        return (x0 - x1) * (x0 - x1) + (y0 - y1) * (y0 - y1);
    }

    public static boolean isRight(int a, int b, int c) {
        if (a == 0 || b == 0 || c == 0) {
            return false;
        }
        if (a == b + c) {
            return true;
        }
        if (b == a + c) {
            return true;
        }
        if (c == a + b) {
            return true;
        }
        return false;
    }

    public static int gcd(int a, int b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    static class FT {

        int[] data;

        FT(int n) {
            data = new int[n];
        }

        void update(int index, int val) {
            // System.out.println("UPDATE INDEX " + index);
            while (index < data.length) {
                data[index] += val;
                index += index & (-index);

                //    System.out.println("NEXT " +index);
            }
        }

        int get(int index) {
            //  System.out.println("GET INDEX " + index);
            int result = 0;
            while (index > 0) {
                result += data[index];
                index -= index & (-index);
                // System.out.println("BACK " + index);
            }
            return result;
        }
    }

    static int pow(int a, int b) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        int val = pow(a, b / 2);
        if (b % 2 == 0) {

            return val * val;
        } else {
            return val * val * a;
        }
    }

//    static Point intersect(Point a, Point b, Point c) {
//        double D = cross(a, b);
//        if (D != 0) {
//            return new Point(cross(c, b) / D, cross(a, c) / D);
//        }
//        return null;
//    }
//
//    static Point convert(Point a, double angle) {
//        double x = a.x * cos(angle) - a.y * sin(angle);
//        double y = a.x * sin(angle) + a.y * cos(angle);
//        return new Point(x, y);
//    }
    static Point minus(Point a, Point b) {
        return new Point(a.x - b.x, a.y - b.y);
    }

    static Point add(Point a, Point b) {
        return new Point(a.x + b.x, a.y + b.y);
    }

    static double cross(Point a, Point b) {
        return a.x * b.y - a.y * b.x;
    }

    static class Point {

        int x, y;

        Point(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public String toString() {
            return "Point: " + x + " " + y;
        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            //System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            //   br = new BufferedReader(new FileReader("input.txt"));
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public String next() {


            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}