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 __future__ import print_function
a,b,x=map(int,raw_input().split())
l=[]
a1=a
b1=b
if(a>=b):
    mini,mini1=b,b
else:
    mini,mini1=a,a
l=[]
l.append(1)
l.append(0)
mini-=1
x-=1
b-=1
a-=1
flag,flag1=1,0
while(mini!=0 and x!=0):
    if(flag==1):
        l.append(1)
        if(mini1==b1):
            mini-=1
            flag1=1
        b-=1
        x-=1
        flag=0
    else:
        l.append(0)
        if(mini1==a1 and flag1==0):
            mini-=1
        a-=1
        x-=1
        flag=1
if(x!=0):
    if(x>1):
        l.insert(0,0)
        a-=1
        x-=1
    if(mini1==a1 and flag1==0):
        for i in range(b):
            l.append(1)
    else:
        if(flag==1):
            for i in range(a):
                l.insert(0,0)
        else:
            for i in range(a):
                l.append(0)
else:
    for i in range(b):
        l.insert(0,1)
    if(flag==1):
        for i in range(a):
            l.append(0)
    else:
        for i in range(a):
            l.insert(len(l)-1,0)
for i in range(len(l)):
    print(l[i],end='')