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 sys,math,heapq,copy
from collections import defaultdict,deque
from bisect import bisect_left,bisect_right
from functools import cmp_to_key
from itertools import permutations,combinations,combinations_with_replacement
# sys.setrecursionlimit(10**6)
# sys.stdin=open('Input.txt','r')
# sys.stdout=open('Output.txt','w')
mod=1000000007
# Reading Single Input
def get_int(): return int(sys.stdin.readline().strip())
def get_str(): return sys.stdin.readline().strip()
def get_float(): return float(sys.stdin.readline().strip())
# Reading Multiple Inputs
def get_ints(): return map(int, sys.stdin.readline().strip().split())
def get_strs(): return map(str, sys.stdin.readline().strip().split())
def get_floats(): return map(float, sys.stdin.readline().strip().split())
# Reading List Of Inputs
def list_ints(): return list(map(int, sys.stdin.readline().strip().split()))
def list_strs(): return list(map(str, sys.stdin.readline().strip().split()))
def list_floats(): return list(map(float, sys.stdin.readline().strip().split()))
# ------------------------------------------------------------------------------------- #

def fun(a,b,ch1,ch2,x):
	ans=""
	ans+=ch1
	a-=1
	for i in range(x):
		if(i==(x-1) and b>0):
			ans+=ch2*b
			b=0
		if(i&1 and a>0):
			ans+=ch1
			a-=1
		elif(b>0):
			ans+=ch2
			b-=1
	if(a>0):
		return ch1*a+ans
	else:
		return ans
a,b,x=get_ints()
if(a>b):
	print(fun(a,b,'0','1',x))
else:
	print(fun(b,a,'1','0',x))