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=str(input())
arr=a.split(' ')
summ=int(arr[0])+int(arr[1])
nul=int(arr[0])#колличество нулей
odin=int(arr[1])#колличество едениц
num=int(arr[2])#колличество "не повторов типа 10 или 01"
chet=num/2-num//2

shablon1='1'
shablon0='0'
shablon='01' if nul>(num+1)//2 else '10'
shablon='10' if odin>(num+1)//2 else '01'


strinn=''
strinnn=''

i=0
if chet>0:
    while i<(num+1)/2:
        strinn=strinn+shablon
        i+=1
else:
    while i<num/2:
        strinn=strinn+shablon
        i+=1
    if strinn[0]=='1':    
        strinn=strinn+shablon1
    else:
        strinn=strinn+shablon0
    
odin=odin-strinn.count('1')
nul=nul-strinn.count('0')
i=0
if strinn[0]=='1':
    if odin>0:
        while i<odin:
            strinn=shablon1+strinn
            i+=1
    
    if nul>0 and strinn[len(strinn)-1]=='0':
        i=0
        while i<nul:
            strinn=strinn+shablon0
            i+=1
    elif nul>0 and strinn[len(strinn)-1]!='0':
        i=0
        while i<nul:
            strinn=strinn[0:len(strinn)-1]+shablon0+shablon1
            i+=1
        
        
else:
    if nul>0:
        while i<nul:
            strinn=shablon0+strinn
            i+=1

    if odin>0 and strinn[len(strinn)-1]=='1':
        i=0
        while i<odin:
            strinn=strinn+shablon1
            i+=1
    elif odin>0 and strinn[len(strinn)-1]!='1':
        i=0
        while i<nul:
            strinn=strinn[0:len(strinn)-1]+shablon1+shablon0
            i+=1

print(strinn)
