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,n=map(int,input().split())
m=n
ans=""
flag=1

if(n>1):
    for i in range(n):
    
        if(flag==1):
            ans=ans+"1"
            
            b=b-1
            flag=0
        else:
            flag=1
            ans=ans+"0"
            a=a-1
    if(ans[-1]=="0"):
        if(b>0):
            
             ans=ans+"0"*a+"1"*b
        
        elif(a>0):
            if(a>0):
                ans="0"+ans+"0"*(a-1)
        
            
    else:
        
        
        if(a>0):
            ans=ans+"1"*b+"0"*a
        else:
            ans="1"+ans+"1"*(b-1)
    print(ans)
else:
    print("1"*b+"0"*a)


        
