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, b, x = map(int, raw_input().split())
zero = a
one = b
answer =[]
count = 0


if(x % 2 == 0):

	if(a > b):
		while(count != x):
			answer.append(0)
			answer.append(1)
			zero -= 1
			one -= 1
			count +=2
		for i in range(one):
			answer.append(1)
		for i in range(zero):
			answer.append(0)
	else:
	
		while(count != x):
			answer.append(1)
			answer.append(0)
			zero -= 1
			one -= 1
			count +=2
		for i in range(zero):

			answer.append(0)		

		for i in range(one):
			answer.append(1)
		

else :	
	if(a > b):
		while count != x + 1:
			answer.append(0)
			answer.append(1)
			zero -= 1
			one -= 1
			count +=2
		for i in range(one):
			answer.append(1)
		for i in range(zero):
			answer.insert(0, 0)

	else:
		while count != x + 1:
			answer.append(1)
			answer.append(0)
			zero -= 1
			one -= 1
			count +=2
		for i in range(zero):
			answer.append(0)
		for i in range(one):
			answer.insert(0, 1)		



string = "".join(str(x) for x in answer)
print(string)




			

