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. 
from sys import stdin,stdout
def main():
    a,b,x = map(int,stdin.readline().split())
    s = []
    x -= 1
    l = 2
    s.append('1')
    s.append('0')
    a -= 1
    b -= 1
    while x:
        x -=1
        if s[0] != s[l-1]:
            if a >= b:
                if s[0] == '0':
                    s.append('0')
                else:
                    s.insert(0,'0')
                a -= 1    
            else:
                if s[0] == '1':
                    s.append('1')
                else:
                    s.insert(0,'1')
                b -= 1
        else:
            if s[l-1] == '0':
                s.append('1')
                b -= 1
            else:
                s.append('0')
                a -= 1
        l += 1
    for i in range(l):
        stdout.write('%s' % s[i])
        if s[i] == '0':
            while a:
                stdout.write('%s' % '0')
                a -= 1
        else:
            while b:
                stdout.write('%s' % '1')
                b -= 1
main()         























