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 int INF = 40;

    public static void main(String[] args) throws IOException {
//        out = new PrintWriter(new File("output.txt"));
//        br = new BufferedReader(new FileReader(new File("input.txt")));
        int GOVNO = 1;
        for (int NASRAL = 0; NASRAL < GOVNO; NASRAL++) {
            int cnt0 = nextInt();
            int cnt1 = nextInt();
            int x = nextInt();
            int max = Math.max(cnt0, cnt1);
            int[] ans = new int[max * 3];
            Arrays.fill(ans, 999);
            int max_ind = 0;
            for (int i = 0; i < Math.max(cnt0, cnt1) * 3; i += 2) {
                ans[i] = 1;
                max--;
                max_ind = i;
                if (max == 0) break;
            }
            int min = Math.min(cnt0, cnt1);
            max = Math.max(cnt0, cnt1);
            for (int i = 1; i < max * 3; i += 2) {
                if (x <= 1) break;
                ans[i] = 0;
                min--;
                x -= 2;
            }
            if (x == 1) {
                for (int i = max_ind + 1; i < max * 3; i++) {
                    ans[i] = 0;
                    min--;
                    if (min == 0) break;
                }
            }
            boolean need = x == 0;
            if (cnt1 > cnt0) {
                for (int i = 0; i < max * 3; i++) {
                    if (ans[i] != 999) {
                        if (ans[i] == 0 && need) {
                            for (int j = 0; j < 1 + min; j++) {
                                out.print(0);
                            }
                            need = false;
                        } else out.print(ans[i]);
                    }
                }
            } else {
                for (int i = 0; i < max * 3; i++) {
                    if (ans[i] != 999) {
                        if (ans[i] == 0) {
                            if (need) {
                                for (int j = 0; j < min + 1; j++) {
                                    out.print(1);
                                }
                                need = false;
                            } else out.print(1);
                        } else out.print(0);
                    }
                }
            }

        }
        out.close();
    }

    static boolean her_one(long a, long st) {
        return (a & st) == st;
    }

    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter out = new PrintWriter(System.out);
    static StringTokenizer in = new StringTokenizer("");


    public static String next() throws IOException {
        while (in == null || !in.hasMoreTokens()) {
            in = new StringTokenizer(br.readLine());
        }
        return in.nextToken();
    }

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

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

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

class Point {
    int ost;
    int ind;

    public Point(int ost, int ind) {
        this.ost = ost;
        this.ind = ind;
    }
}