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= [int(x) for x in raw_input().split()]

aBigger = a >= b

ans = [0] * max(a,b)

const = 0 
cnt = -1
if x % 2 == 1:
    ans.append(1)
    cnt = cnt - 1
    if (aBigger):
        b = b - 1
    else:
        a = a - 1
    

for i in range(x / 2):
    ans.insert(cnt, 1)
    cnt = cnt - 2
    if (aBigger):
        b = b - 1
    else:
        a = a - 1

if aBigger:
    for i in range(b):
       ans.insert(-1, 1)
else:
    for i in range(a):
        ans.insert(-1, 1)

if not aBigger:
    ans = "".join(map(str,ans))
    ans = ans.replace("1", ".")
    ans = ans.replace("0", "1")
    ans = ans.replace(".", "0")
else:
    ans = "".join(map(str,ans))
    
print(ans)
    
