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. 
from math import ceil

t = 1
for test in range(t):
    a,b,x = map(int, input().split())
    if a+b == 1:
        print("0"*a+"1"*b)
    else:
        arr = [""]
        if a>b:
            for i in range(a):
                arr.append("0")
                arr.append("")
            if x%2==0:
                for i in range(1, x//2+1):
                    arr[i*2] = "1"
                    b-=1
                arr[x//2]=arr[x//2]+"1"*b
            else:
                for i in range(x//2+1):
                    arr[i*2] = "1"
                    b-=1
                arr[x//2]=arr[x//2]+"1"*b
        else:
            for i in range(b):
                arr.append("1")
                arr.append("")
            if x%2==0:
                for i in range(1, x//2+1):
                    arr[i*2] = "0"
                    a-=1
                arr[x//2]=arr[x//2]+"0"*a
            else:
                for i in range(x//2+1):
                    arr[i*2] = "0"
                    a-=1
                arr[x//2]=arr[x//2]+"0"*a
    for i in arr:
        print(i, end="")
    print()

