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())
mn = '0' if a < b else '1'
mx = '0' if a >= b else '1'
f= False
r = mx
if mx == '0':
    a -= 1
else:
    b -= 1
for i in range(x):
    if f:
        r += mx
        if mx == '0':
            a -= 1
        else:
            b -= 1
    else:
        r += mn
        if mn == '0':
            a -= 1
        else:
            b -= 1
    f = not f
r = r.replace('0', '0'*(a+1), 1)
r = r.replace('1', '1'*(b+1), 1)
print(r)