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. 
def constructBinString(a, b, x):  
  
    d = x // 2
  

    if x % 2 == 0 and x // 2 != a:  
        d -= 1
        print("0", end = "")  
        a -= 1
  

    for i in range(d):  
        print("10", end = "")  
  
   
    a = a - d  
    b = b - d  
  
   
    for i in range(b):  
        print("1", end = "") 
      
   
    for i in range(a):  
        print("0", end = "") 
  
# Driver Code 
if __name__ == "__main__":  
  
    a,b,x=map(int, input().split())
    constructBinString(a, b, x) 
