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. 
w=input().split()
b=int(w[0])
a=int(w[1])
x=int(w[2])

ans=""
last=''
for i in range(a+b):
	if a>=b and last=='':
		#print("hi")
		ans=ans+'1'
		a=a-1
		last='1'
	elif b>a and last=='':
		ans=ans+'0'
		b=b-1
		last='0'

	elif last=='1':
		if x>a and b>0:
			ans=ans+'0'
			b=b-1
			x=x-1
			last='0'
		else:
			ans=ans+'1'
			a=a-1

	elif last=='0':
		if x>b and a>0:
			ans=ans+'1'
			a=a-1
			x=x-1
			last='1'
		else:
			ans=ans+'0'
			b=b-1
print(ans)















