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. 

s=input()
s=s.split(" ")
for i in range(len(s)):
    s[i]=int(s[i])

a=s[0]
b=s[1]
x=s[2]
compt=0
resu=""

if a<b:
    while compt<x:
        resu=resu+"10"
        compt=compt+2
    na =( a-compt//2 ) 
    nb =( b-compt//2 ) 
   
    if x%2==1:
         resu= nb * "1"  +resu + na* "0"
    else:
        if na==0:
            resu= resu + nb* "1"
        else:
            resu= "0" + nb * "1"  +resu + (na-1)* "0"
    

else:
    while compt<x:
        resu=resu+"01"
        compt=compt+2
        na =( a-compt//2 ) 
        nb =( b-compt//2 ) 
    if x%2==1:
        resu= na * "0"  +resu + nb* "1"
    else:
        if nb==0:
            resu= resu + na* "0"
        else:
            resu= "1" + na * "0"  +resu +( nb-1)* "1"
        
    
    
print(resu)