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. 
#codeforces_1003B_live
a,b,x = [int(e) for e in input().split(" ")]
ans = ""
choose = ["0","1"]
if x == 1:
	print(a*"0"+b*"1")
	exit()
if x == 2:
	if (b>1):
		print((b-1)*"1"+a*"0"+"1")
	else:
		print((a-1)*"0"+b*"1"+"0")
	exit()
if x == 3:
	print((b-2)*"1"+"101"+(a-1)*"0")
	exit()
while x > 1:
	ans += choose[x%2]
	if (x%2 == 0): a-=1;
	if (x%2 == 1): b-=1;
	x -= 1
'''
print(ans)
print(a)
print(b)
'''
if ans[-1] == "0":
	if a == 0:
		ans = "1" + ans + (b-1)*"1"
	else:
		ans = ans + "1"*(b) + "0"*(a)
else:
	ans = ans + "0"*a + "1"*b
print(ans)
