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. 
b, a, x = list( map( int, input().split(' ')) )
def rec(a, b, x, chars):
    if a < 0 or b < 0 or x < 0:
        return False
    if a==0 and b==0 and x==0:
        print(chars)
        return True
    if x > 1:
        if chars[-1] == '1':
            return rec(a, b-1, x-1, chars+'0')
        else:
            return rec(a-1, b, x-1, chars+'1')
    if x == 1:
        if chars[-1] == '1':
            if a > 0:
                return rec(a-1, b, x, chars+'1')
            elif b > 0:
                return rec(a, b-1, x-1, chars+'0')
            else:
                return False
        else:
            if b > 0:
                return rec(a, b-1, x, chars+'0')
            elif a > 0:
                return rec(a-1, b, x-1, chars+'1')
            else:
                return False
    if x==0:
        if chars[-1] == '1' and b == 0:
            return rec( a-1, b, x, chars+'1')
        elif chars[-1] == '0' and a == 0:
            return rec( a, b-1, x, chars+'0')
    return False

if rec( a-1, b, x, '1') or rec( a, b-1, x, '0'):
    pass

