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. 
#!/usr/bin/env python3
from sys import stdin


def solve(tc):
    # items = map(int,stdin.readline().split())
    a, b, x = map(int, stdin.readline().split())

    if a>b:
        c = 0
    else:
        c = 1
    
    s = ""
    for i in range(0,x-1):
        s += str(c)
        if c==0:
            a -= 1
        else:
            b -= 1
        c ^= 1
    
    if c==0:
        s += '0'*a
        s += '1'*b
    else:
        s += '1'*b
        s += '0'*a
    print(s)


LOCAL_TEST = not __debug__
if LOCAL_TEST:
    infile = __file__.split('.')[0] + "-test.in"
    stdin = open(infile, 'r')

tcs = (int(stdin.readline().strip()) if LOCAL_TEST else 1)
tc = 1
while tc <= tcs:
    solve(tc)
    tc += 1