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. 
p, q, x = map(int,input().split())

if x == 1 :
    print('0' * p, end = '')
    print('1' * q, end = '')
    
else :
    if p > q :
        l = '0'
        h = '1'
        a = p - 1
        b = q - 1
    else :
        h = '0'
        l = '1'
        a = q - 1 
        b = p - 1
    print(l, end = '')
    print(h, end = '')
    flag = -1
    x -= 1

    while x > 1 :
        if a > 0 :
            print(l, end = '')
            x -= 1
            a -= 1
            flag = 0
        if b > 0 and x != 1:
            print(h, end = '')
            x -= 1
            b -= 1
            flag = 1
    if flag == 0 :
        print(l * a, end = '')
        print(h * b, end = '')
    
    else :
        print(h * b, end = '')
        print(l * a, end = '')
    