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 itertools import product, permutations, combinations, combinations_with_replacement
# from itertools import chain, compress, starmap, count, cycle, repeat
import itertools

def s(s, l, x, y1, y2):
    t = [y2, y1] * (x // 2)
    n_x = (x // 2) * 2 - 1
    if n_x < 0 : n_x = 0
    if x - n_x == 2:
        t += [y2, y1]
        num_each = len(t) // 2
        t += [y1] * (s - num_each)
        t = [y2] * (l - num_each) + t
    elif x - n_x == 1:
        num_each = len(t) // 2
        t += [y1] * (s - num_each)
        t += [y2] * (l - num_each)
    elif x - n_x == 0:
        num_each = len(t) // 2
        t += [y1] * (s - num_each)
        t = ([y2] * (l - num_each)) + t

    print(''.join(t))

def solution(a, b, x):
    if a < b:
        s(a, b, x, '0', '1')
    else:
        s(b, a, x, '1', '0')

def main():
    import sys
    a, b, x = map(int, sys.stdin.read().split())
    # length, period, tides = lines
    # length = 10
    # period = 9
    # tides = '1........1'
    solution(a, b, x)
    # line = '1.0.1.1.1.1.0.'


main()
