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. 
j=(input()).split(" ")
a=int(j[0])
b=int(j[1])
x=int(j[2])
s=""
if (a>b):
    s+="0"
    a-=1

else:
    s+="1"
    b-=1
    
while (x>1):
    if (s[len(s)-1]=="0"):
        b-=1
        s+="1"
    else:
        a-=1
        s+="0"
    x-=1
#print(s)
    
if (x==1):
    if (s[len(s)-1]=="1"):
        s+="1"*b+"0"*a
        a=0
        b=0
    else:
        s+="0"*a+"1"*b
        a=0
        b=0
        
if (x==0):
    if (s[len(s)-1]=="0"):
        s+="0"*a
        a=0
    else:
        s+="1"*b
        b=0
    s="1"*b+"0"*a+s;


print(s)


