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. 
class CodeforcesTask1003BSolution:
    def __init__(self):
        self.result = ''
        self.a_b_x = []

    def read_input(self):
        self.a_b_x = [int(x) for x in input().split(" ")]

    def process_task(self):
        result = []
        starting = "0" if self.a_b_x[0] >= self.a_b_x[1] else "1"
        second = "1" if self.a_b_x[0] >= self.a_b_x[1] else "0"
        c = True
        for x in range(self.a_b_x[2] - 1):
            if c:
                result.append(starting)
                c = not c
                if starting == "0":
                    self.a_b_x[0] -= 1
                else:
                    self.a_b_x[1] -= 1
            else:
                result.append(second)
                c = not c
                if second == "0":
                    self.a_b_x[0] -= 1
                else:
                    self.a_b_x[1] -= 1
        if c:
            if starting == "0":
                result.append(starting * self.a_b_x[0])
                result.append(second * self.a_b_x[1])
            else:
                result.append(starting * self.a_b_x[1])
                result.append(second * self.a_b_x[0])
        else:
            if starting == "0":
                result.append(second * self.a_b_x[1])
                result.append(starting * self.a_b_x[0])
            else:
                result.append(second * self.a_b_x[0])
                result.append(starting * self.a_b_x[1])
        self.result = "".join(result)

    def get_result(self):
        return self.result


if __name__ == "__main__":
    Solution = CodeforcesTask1003BSolution()
    Solution.read_input()
    Solution.process_task()
    print(Solution.get_result())
