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 binary_str():
    inp = list(map(int, input().split()))
    zeros_num = inp[0]
    ones_num = inp[1]
    indexes_num = inp[2]
    ones_count = 0
    zeros_count = 0
    order = True
    if zeros_num < ones_num:
        zeros_num, ones_num = ones_num, zeros_num
        order = False

    if indexes_num % 2 != 0:
        toggle = False
        middle = '1'
        ones_count += 1
    else:
        toggle = True
        middle = '0'
        zeros_count += 1

    for i in range(indexes_num):
        if toggle is True and ones_count < ones_num:
            middle += '1'
            ones_count += 1
            toggle = False
        elif toggle is False and zeros_count < zeros_num:
            middle += '0'
            zeros_count += 1
            toggle = True

    border1 = middle.index('1')
    border0 = middle.index('0')
    insert_ones = '1' * (ones_num - ones_count)
    insert_zeros = '0' * (zeros_num - zeros_count)
    if border1 < border0:
        res = middle[:border1+1] + insert_ones + middle[border1+1:border0+1] + insert_zeros + middle[border0+1:]
    else:
        res = middle[:border0 + 1] + insert_zeros + middle[border0 + 1:border1 + 1] + insert_ones + middle[border1 + 1:]
    if order is False:
        res = res.replace('1', 'a')
        res = res.replace('0', '1')
        res = res.replace('a', '0')
    return res

print(binary_str())