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 = map(int,raw_input().split())
a = p[0]
b = p[1]
x = p[2]
bc = b
ac = a
if(a>b):
    s = "0"
    ac-=1
else:
    s = "1"
    bc-=1

xc = x

while(xc):
    if(s[-1] == "0"):
        if(bc):
            s+="1"
            bc-=1
        else:
            s+="0"
            ac-=1
    else:
        if(ac):
            s+="0"
            ac-=1
        else:
            s+="1"
            bc-=1
    xc-=1

sw = ""
for i in s:
    if(i == "0"):
        sw += i
        if(ac):
            sw += "0"*ac
            ac = 0
    else:
        sw += i
        if(bc):
            sw += "1"*bc
            bc = 0

print sw

