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. 
n=input()
c=''
n=n.split()
b=int(n[0])
a=int(n[1])
x=int(n[2])
if x==2*a:
    for i in range(a):
        c+='01'
    for i in range(b-a):
        c+='0'
if x==2*b:
    for i in range(b):
        c+='10'
    for i in range(a-b):
        c+='1'
if  x<2*b and x<2*a:
    if x%2==1:
        for i in range(a-(x+1)//2):
            c+='1'
        for i in range((x+1)//2):
            c+='10'
        for i in range(b-(x+1)//2):
            c+='0'
    else:
        if a>b:
            for i in range(a-(x+1)//2-1):
                c+='1'
            for i in range((x+1)//2):
                c+='10'
            for i in range(b-(x+1)//2):
                c+='0'
            c+='1'
        else:
            c+='0'
            for i in range(a-(x)//2):
                c+='1'
            for i in range((x)//2):
                c+='10'
            for i in range(b-(x)//2-1):
                c+='0'
print(c)
