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(i) for i in input().split()]

one = b
zero = a
if a>=b:
    print(0,end="")
    zero-=1
    a=0
else:
    print(1, end="")
    one -= 1
    a = 1
for i in range(one+zero):
    if x>1:
        if a==1:
            print(0, end="")
            x-=1
            zero-=1
            a=0
        else:
            print(1, end="")
            x-=1
            one-=1
            a=1
if x==1:
    if a==1:
        while one>0:
            print(1,end="")
            one-=1
        while zero>0:
            print(0,end="")
            zero-=1
    if a==0:
        while zero>0:
            print(0,end="")
            zero-=1
        while one>0:
            print(1,end="")
            one-=1










































