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 = [int(i) for i in input().split()]

if(a > b):
    maxD = "0"
    maxN = a
    minD = "1"
    minN = b
else:
    maxD = "1"
    maxN = b
    minD = "0"
    minN = a

s = [str(maxD)]*(a + b)

c = 0
if(x%2==0):
    for i in range(x):
        if(i%2==1):
            s[i] = minD
            c+=1
            k=i
else:
    for i in range(x):
        if(i%2==0):
            s[i] = minD
            c+=1
            k=i

while(c < minN):
    k += 1
    s[k] = minD
    c+=1

print("".join(s))