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, os
# import numpy as np
from math import sqrt, gcd, ceil, log, floor, sin, pi
from math import factorial as fact
from bisect import bisect, bisect_left
from collections import defaultdict, Counter, deque
from heapq import heapify, heappush, heappop
from itertools import permutations
input = sys.stdin.readline
read = lambda: list(map(int, input().strip().split()))
# read_f = lambda file:  list(map(int, file.readline().strip().split()))
# from time import time
# sys.setrecursionlimit(5*10**6)

MOD = 10**9 + 7



def main():
	# file1 = open("C:\\Users\\shank\\Desktop\\Comp_Code\\input.txt", "r")
	# n = int(file1.readline().strip()); 
	# par = list(map(int, file1.read().strip().split(" ")))
	# file1.close()
	# ans_ = []
	# for _ in range(int(input())):
	a, b, x = read()
	if a >= b:pat = "01"
	else:pat = "10"
	ans = (pat*(x//2 + 1))[:x+1]
	x, y = a-ans.count("0")+1, b-ans.count("1")+1
	ans = list(ans)
	ans[ans.index("0")] = "0"*x
	ans[ans.index("1")] = "1"*y
	ans = ("").join(ans)
	print(ans)
	# s = 0
	# for i in range(a+b-1):
	# 	s += ans[i] != ans[i+1]
	# print(s)






	# for i in ans_:print(i)

	# file = open("output.txt", "w")
	# file.write(ans+"\n")
	# file.close()

if __name__ == "__main__":
	main()



"""



"""