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. 

def f(a,b,x):
    s = []
    if x % 2 == 0:
        if a >= b:
            while x > 0:
                s.append(0)
                s.append(1)
                x -= 2
                a -= 1
                b -= 1
            while b > 0:
                s.append(1)
                b -= 1
            while a > 0:
                s.append(0)
                a -= 1
        if b > a:
            while x > 0:
                s.append(1)
                s.append(0)
                x -= 2
                a -= 1
                b -= 1
            while a > 0:
                s.append(0)
                a -= 1               
            while b > 0:
                s.append(1)
                b -= 1
    else:
        if a >= b:
            while x > 1:
                s.append(0)
                s.append(1)
                x -= 2
                a -= 1
                b -= 1
            while a > 0:
                s.append(0)
                a -= 1            
            while b > 0:
                s.append(1)
                b -= 1
            
        if b > a:
            while x > 1:
                s.append(1)
                s.append(0)
                x -= 2
                a -= 1
                b -= 1
            while b > 0:
                s.append(1)
                b -= 1              
            while a > 0:
                s.append(0)
                a -= 1               
                  
                
    return ''.join(str(x) for x in s)

a,b,x = [int(i) for i in input().split()]
print(f(a,b,x))