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. 
alist = list(map(int,input().split()))
a,b,x = alist[0],alist[1],alist[2]
def probin(x,temp):
    string = ''
    for i in range(x+1):
        string+=str(temp)
        temp = abs(temp-1)
    return string
###########################
if x % 2 != 0:#dan
    a -= (x+1)/2
    b -= (x+1)/2
    if a >= 0 and b >= 0:
        string = probin(x, 1)
        string = '1' * int(b) + string
        string = string + '0' * int(a)
    else:
        string = probin(x,0)
        string = string + '1' * int(b)
        string = '0' * int(a) + string
else:#shuang
    a1 =a - x/2
    b1 =b - (x+2)/2
    if a1 >= 0 and b1 >= 0:
        string = probin(x, 1)
        string = '1' * int(b1) + string
        string = string[:-1] + '0' * int(a1) + '1'
    else:
        string = probin(x, 0)
        a2 = a - (x+2)/2
        b2 = b - x/2
        string = string[:-1] + '1' * int(b2) + '0'
        string = '0' * int(a2) + string
print(string)