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. 
read = input()
a , b, x = map(int ,read.split())

s = ""
bo = True
car1 = '0'
car2 = '1'

if b > a:
    aux = a
    a = b
    b = aux
    car1 = '1'
    car2 = '0'

if a > 0:
    s = s+car1
    a = a-1
elif b > 0:
    s = s+car2
    b = b-1
    bo = False

while x > 0:
    if bo:
        s = s+car2
        bo = False
        b = b-1
    else:
        s = s+car1
        bo = True
        a = a-1
    x = x - 1

# print(s)

tmp = ""
while b > 0:
    tmp = tmp+car2
    b = b-1
# print(tmp)

if len(s) > 0:
    s = car1+ tmp + s[1:]


tmp = ""
while a > 0:
    tmp = tmp+car1
    a  =a-1
s = tmp + s
print(s)
