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.util.*;
import java.io.*;
import java.math.*;

public class Test5 {

    static int a, b, x, o=0;
    static int[] m, n;

    public static void main(String[] jk) throws Exception{
        PrintWriter pw = new PrintWriter(System.out);
        StreamTokenizer st = new StreamTokenizer(new InputStreamReader(System.in));
        Scanner s = new Scanner(System.in);
        a = s.nextInt();
        b = s.nextInt();
        x = s.nextInt();
        String o= a>b ? 0+"" : 1+"";
        if(a>b) a--;
        else b--;
        char p, str = o.charAt(0);
        if(x==1){
            if(str=='0') {
                for (; a > 0; a--) o += 0;
                for (; b > 0; b--) o += 1;
            }
            else{
                for (; b > 0; b--) o += 1;
                for (; a > 0; a--) o += 0;
            }
        }
        else {
            for (int q = 0; q < x - 1; q++) {
                if(o.charAt(o.length()-1)=='0'){
                    o+=1;
                    b--;
                }
                else{
                    o+=0;
                    a--;
                }
            }
            p = o.charAt(o.length() - 1);
            if (a > 0 & b > 0) {
                if (p == '0') {
                    for (; a > 0; a--) o += 0;
                    for (; b > 0; b--) o += 1;
                } else {
                    for (; b > 0; b--) o += 1;
                    for (; a > 0; a--) o += 0;
                }
            } else if (a > 0) {
                if (p == '1') for (; a > 0; a--) o += 0;
            } else if (b > 0) {
                if (p == '0') for (; b > 0; b--) o += 1;
            }
        }
        System.out.println(o);
        pw.flush();
    }

    static int f(){
        return 0;
    }

    static class PyraSort {

        private static int heapSize;

        public static void sort(int[] a) {
            buildHeap(a);
            while (heapSize > 1) {
                swap(a, 0, heapSize - 1);
                heapSize--;
                heapify(a, 0);
            }
        }

        private static void buildHeap(int[] a) {
            heapSize = a.length;
            for (int i = a.length / 2; i >= 0; i--) {
                heapify(a, i);
            }
        }

        private static void heapify(int[] a, int i) {
            int l = 2 * i + 2;
            int r = 2 * i + 1;
            int largest = i;
            if (l < heapSize && a[i] < a[l]) {
                largest = l;
            }
            if (r < heapSize && a[largest] < a[r]) {
                largest = r;
            }
            if (i != largest) {
                swap(a, i, largest);
                heapify(a, largest);
            }
        }

        private static void swap(int[] a, int i, int j) {
            a[i] ^= a[j] ^= a[i];
            a[j] ^= a[i];
        }
    }
}
