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 {
    static InputStream inputStream = System.in;
    static OutputStream outputStream = System.out;
    static InputReader in = new InputReader(inputStream);
    static PrintWriter out = new PrintWriter(outputStream);

    public static void main(String[] args) throws IOException {
        int t = 1;
        while (t-- > 0) {
            solve();
        }
        out.close();

    }

    private static void solve() {
        int a = in.nextInt();
        int b = in.nextInt();
        int x = in.nextInt();
        String str = "";
        int i = 0;
        if (a >= b) {
            str = str + "0";
            a--;
        } else {
            str = str + "1";
            b--;
        }
        i++;
        while (x > 1) {
            if (str.charAt(i - 1) == '0') {
                str = str + "1";
                b--;
            } else {
                str = str + "0";
                a--;
            }
            x--;
            i++;
        }
        if (str.charAt(i - 1) == '0') {
            while (a-- > 0) {
                str = str + "0";
            }
            while (b-- > 0) {
                str = str + "1";

            }
        } else {
            while (b-- > 0) {
                str = str + "1";
            }
            while (a-- > 0) {
                str = str + "0";
            }
        }
        out.println(str);

    }

    private static void solve1() {
        int n = in.nextInt();
        int k = in.nextInt();
        int[] pref = new int[n + 1];
        int[] arr = new int[n + 1];
        for (int i = 0; i < n; i++) {
            arr[i] = in.nextInt();
            pref[i + 1] = pref[i] + arr[i];
        }
        double ans = 0;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < i + 1; j++) {
                if (i - j + 1 >= k) {
                    ans = (double) Math.max(ans, (pref[i + 1] - pref[j]) / (double) (i - j + 1));
                }
            }
        }
        System.out.println((double) Math.round(ans * 1000000000000000d) / 1000000000000000d);

    }

    private static void sort(int[] arr) {
        int n = arr.length;
        ArrayList<Integer> res = new ArrayList<>();
        for (int a : arr) {
            res.add(a);
        }
        Collections.sort(res);
        for (int i = 0; i < n; i++) {
            arr[i] = res.get(i);
        }
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

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

        public String nextLine() throws IOException {
            return reader.readLine().trim();
        }
    }
}