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. 
#Round 494
#B
from sys import stdin, stdout

def main():
    a, b, x = [int(i) for i in stdin.readline().split()]
    arr = [""]*(x+1)
    a_char = "0"
    b_char = "1"
    if b > a:
        a, b = b, a
        a_char, b_char = b_char, a_char
    for i in range(x+1):
        if i >= x-1:
            if i%2 == 0:
                arr[i] = a_char*a
            else:
                arr[i] = b_char*b
        else:
            if i%2 == 0:
                arr[i] = a_char
                a -= 1
            else:
                arr[i] = b_char
                b -= 1

    stdout.write("".join(arr) + "\n")
    
    
main()

