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. 
[a,b,x] = map(int, raw_input().strip().split())
flag = 1
if b > a:
    c = a
    a = b
    b = c
    flag = 0

s = [0]*a

pos = 1
while ((x > 0) or  (b > 0)):
    if x == 0:
        if pos == 1:
            pos = 2
        s.insert(pos-2,1)
        b -= 1
    elif x == 1:
        s.insert(0,1)
        b -= 1
        x -= 1
    elif x >= 2:
        s.insert(pos,1)
        pos += 2
        b -= 1
        x -= 2

    #print "x=",x, "b=",b, "pos=",pos, s

if flag == 0:
    for i in range(len(s)):
        s[i] = abs(s[i]-1)

print ''.join(str(x) for x in s)

