You are given three integers a, b and x. Your task is to construct a binary string s of length n = a + b such that there are exactly a zeroes, exactly b ones and exactly x indices i (where 1 ≤ i < n) such that s_i ≠ s_{i + 1}. It is guaranteed that the answer always exists.

For example, for the string "01010" there are four indices i such that 1 ≤ i < n and s_i ≠ s_{i + 1} (i = 1, 2, 3, 4). For the string "111001" there are two such indices i (i = 3, 5).

Recall that binary string is a non-empty sequence of characters where each character is either 0 or 1.

Input

The first line of the input contains three integers a, b and x (1 ≤ a, b ≤ 100, 1 ≤ x < a + b).

Output

Print only one string s, where s is any binary string satisfying conditions described above. It is guaranteed that the answer always exists.

Examples

Input

2 2 1


Output

1100


Input

3 3 3


Output

101100


Input

5 3 6


Output

01010100

Note

All possible answers for the first example: 

  * 1100; 
  * 0011. 



All possible answers for the second example: 

  * 110100; 
  * 101100; 
  * 110010; 
  * 100110; 
  * 011001; 
  * 001101; 
  * 010011; 
  * 001011. 
import java.io.*;
import java.util.*;

public class Main {
    void solve(FastScanner in, PrintWriter out) throws IOException {
        int a = in.nextInt();
        int b = in.nextInt();
        int x = in.nextInt();
        if (x % 2 == 0) {
            if (a > b) {
                for (int i = 0; i < x / 2; ++i)
                    out.print("01");
                out.print(string(b - x / 2, '1'));
                out.print(string(a - x / 2, '0'));
            } else {
                for (int i = 0; i < x / 2; ++i)
                    out.print("10");
                out.print(string(a - x / 2, '0'));
                out.print(string(b - x / 2, '1'));
            }
        } else if (a > b) {
            for (int i = 0; i < x / 2; ++i)
                out.print("01");
            out.print(string(a - x / 2, '0'));
            out.print(string(b - x / 2, '1'));
        } else {
            for (int i = 0; i < x / 2; ++i)
                out.print("10");
            out.print(string(b - x / 2, '1'));
            out.print(string(a - x / 2, '0'));
        }
    }

    String string(int k, char c) {
        StringBuilder builder = new StringBuilder();
        for (int i = 0; i < k; i++) {
            builder.append(c);
        }
        return builder.toString();
    }

    public static void main(String[] args) throws IOException {
//        FastScanner in = new FastScanner(new FileReader("input.txt"));
//        PrintWriter out = new PrintWriter(new FileWriter("output.txt"));
        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        new Main().solve(in, out);
        out.close();
    }

    static class FastScanner {
        StringTokenizer st;
        BufferedReader br;

        public FastScanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public FastScanner(FileReader f) {
            br = new BufferedReader(f);
        }

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

        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        public boolean hasNext() {
            return st.hasMoreElements();
        }

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

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

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

        public boolean nextBoolean() {
            return Boolean.parseBoolean(next());
        }

        public void close() throws IOException {
            br.close();
        }
    }
}