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. 
# cook your dish here

#from math import factorial, ceil, pow, sqrt, floor, gcd
from sys import stdin, stdout
from collections import defaultdict, Counter, deque
#from bisect import bisect_left, bisect_right
#import sympy
#from itertools import permutations
#import numpy as np

#           n = int(stdin.readline())
#           stdout.write(str())
#           s = stdin.readline().strip('\n')
#           map(int, stdin.readline().split())
#           l = list(map(int, stdin.readline().split()))

for _ in range(1):
    a, b, x = map(int, stdin.readline().split())
    s = []
    c,d = a,b

    while x>0 and (a >c - min(c,d) or b > d-min(c,d)):
        if len(s)==0:
            s.append('1')
            b -= 1
        if s[-1] == '1':
            s.append('0')
            x -= 1
            a -= 1
        else:
            s.append('1')
            x -= 1
            b -= 1

    s = ''.join(e for e in s)

    if x!=0:
        if a>0:
            s = '0'+s
            a -= 1
        else:
            s += '1'
            b -= 1

    s = '1'*(b) + s
    if s[-1]=='0':
        s += '0'*a
    else:
        s = s[:len(s)-1] + '0'*a + s[-1]

    stdout.write(s+'\n')
