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 = map(int, input().split())

m1, m2 = max(a,b), min(a,b)
m1c = '0' if m1 == a else '1'
m2c = '1' if m1c == '0' else '0'

s = ''
is_m1 = True
while x > 0:
    x = x-1 if len(s) > 0 else x
    s += m1c if is_m1 else m2c
    if is_m1:
        m1 -= 1
    else:
        m2 -= 1
    is_m1 = not is_m1

if m2 > 0:
    if is_m1:
        s = s + m2c * m2
    else:
        s = s[:-1] + m2c * m2 + s[-1]

if m1 > 0:
    s = m1c * m1 + s

print(s)