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. 
#Imports
from sys import stdin, stdout
from collections import Counter

#Aux
def _find_binary_string(num_zeros, num_ones, num_distinct_adj):
    remainder = num_distinct_adj%2
    repeated_times = (num_distinct_adj+remainder)/2
    repeated_str = "10"*repeated_times
    num_zeros -= repeated_times
    num_ones -= repeated_times

    zeros = "0"*num_zeros
    ones = "1"*num_ones

    if remainder == 0:
        if num_ones > 0:
            return repeated_str + zeros + ones
        else:
            return "0" + repeated_str + zeros[:-1]
    else:
        return ones + repeated_str + zeros


#Main
def _main():

    #Read input
    num_zeros, num_ones, num_distinct_adj = [int(x) for x in stdin.readline().rstrip().split()]


    #Calculate answer
    ans = _find_binary_string(num_zeros, num_ones, num_distinct_adj)


    #Print output
    stdout.write(ans)


#Call
_main()