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 main():
    a, b, x = map(int, input().split())
    
    for st in "01":
        s = st
        while (len(s) <= x):
            if (s[-1] == "0"):
                s += "1"
            else:
                s += "0"
        aa = a - s.count("0")
        bb = b - s.count("1")
        if (aa < 0 or bb < 0):
            continue
        else:
            while (aa > 0):
                pos = s.index("0")
                s = s[:pos] + "0" + s[pos:]
                aa -= 1
            while (bb > 0):
                pos = s.index("1")
                s = s[:pos] + "1" + s[pos:]
                bb -= 1
            print(s)
            return
        
main()