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. 

entrada = input()
entrada = entrada.split(' ')

a = int(entrada[0]) # zeroes
b = int(entrada[1]) # ones
x = int(entrada[2]) # x = |s|, s = forall(ai != ai+1)

"""
1 <= a, b <= 100, 1 <= 1 < a+b

2 2 1
1100
______________
0011

3 3 3
101100
______________
001011

5 3 6
01010100
______________
0101010
"""

string = ""
if a >= b:
    last = 0
    string += '0'
    a -= 1
    while x > 0:
        
        if last == 0:
            b -= 1
        else:    
            a -= 1
        
        last = ( last + 1 ) % 2
        string += str( last )
        x -= 1

    string = string[0] + a*'0' + string[1:len(string)]
    string = string[0:a+1] + b*'1' + string[a+1:len(string)]
else:
    last = 1
    string += '1'
    b -= 1
    while x > 0:
        
        if last == 0:
            b -= 1
        else:
            a -= 1

        last = ( last + 1 ) % 2
        string += str( last )
        x -= 1
    
    string = string[0] + b*'1' + string[1:len(string)]
    string = string[0:b+1] + a*'0' + string[b+1:len(string)]

print(string)