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. 
a_b_x = input()
a_b_x = [int(i) for i in a_b_x.split(' ')]

answer = ''
previous_digit = 0
for i in range(a_b_x[0] + a_b_x[1]):
    if i == 0:    
        answer += '0'
        a_b_x[0] -= 1
    else:
        if a_b_x[2] > 1:
            if previous_digit == 0:
                answer += '1'
                a_b_x[2] -= 1
                a_b_x[1] -= 1
                previous_digit = 1
            else:
                answer += '0'
                a_b_x[2] -= 1
                a_b_x[0] -= 1
                previous_digit = 0
        elif a_b_x[2] == 1:
            if previous_digit == 0:
                if a_b_x[0] > 0:
                    answer += '0'
                    a_b_x[0] -= 1
                    previous_digit = 0
                else:
                    answer += '1'
                    a_b_x[1] -= 1
                    a_b_x[2] -= 1
                    previous_digit = 1
            else:
                if a_b_x[1] > 0:
                    if a_b_x[1] > 1:
                        answer += '1'
                        a_b_x[1] -= 1
                        previous_digit = 1
                    elif a_b_x[1] == 1 and a_b_x[0] == 0:
                        answer = '1' + answer
                        a_b_x[1] -= 1
                        previous_digit = 1
                    else:
                        answer += '1'
                        a_b_x[1] -= 1
                        previous_digit = 1
                else:
                    answer += '0'
                    a_b_x[0] -= 1
                    a_b_x[2] -= 1
                    previous_digit = 0
        else:
            if previous_digit == 0:
                answer += '0'
                a_b_x[0] -= 1
                previous_digit = 0
            else:
                answer += '1'
                a_b_x[1] -= 1
                previous_digit = 1

print(answer)
