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. 
#      
import collections
from functools import cmp_to_key
#key=cmp_to_key(lambda x,y: 1 if x not in y else -1 )
import math
import sys
def getIntList():
    return list(map(int, input().split()))    

import bisect 
try :
    import numpy
    dprint = print
    dprint('debug mode')
except ModuleNotFoundError:
    def dprint(*args, **kwargs):
        pass
def makePair(z):
    return  [(z[i], z[i+1]) for i in range(0,len(z),2) ]
def memo(func):  
    cache={}  
    def wrap(*args):  
        if args not in cache:  
            cache[args]=func(*args)  
        return cache[args]  
    return wrap

@memo
def comb (n,k):
    if k==0: return 1
    if n==k: return 1
    return comb(n-1,k-1) + comb(n-1,k)

a,b,x = getIntList() 

if x ==1:
    z = [0] * a
elif a< b:
    z= [1]
    b-=1
else:
    a-=1
    z = [0]

while x>0:
    if z[-1] ==0:
        z.append(1)
        b-=1
        if x<=2:
            
            z.extend( [1] * b)
    else:
        z.append(0)
        a-=1
        if x<=2:
            z.extend( [0] * a)        
    x-=1

for x in z:
 
    print(x, end ='')
 
