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. 
a1=input()
b1=a1.split()
a=int(b1[0])
b=int(b1[1])
x=int(b1[2])
m=''
n=''
ans=''
for i in range(a):
	m+='0'
for j in range(b):
	n+='1'
if (x%2==0):
	o=x//2
	c0=a
	c1=b
	if (a>=b):
		ans=m
	else:
		ans=n
	z=len(ans)-1
	for k in range(o-1):
		c=0
		while (c<z):
			if (a>=b):
				if (ans[c]==ans[c+1]):
					ans=ans[:c+1]+'1'+ans[c+1:]
					c1-=1
					z+=1
					
					break
				c+=1
			else:
				if (ans[c]==ans[c+1]):
					ans=ans[:c+1]+'0'+ans[c+1:]
					z+=1
					c0-=1
					c+=1
					break
				c+=1
	for l in range(len(ans)-1):
		if (a>=b):
			if (ans[l]==ans[l+1]):
				p=''
				for i in range(c1):
					p+='1'
				ans=ans[:l+1]+p+ans[l+1:]
				break
		else:
			if (ans[l]==ans[l+1]):
				p=''
				for i in range(c0):
					p+='0'
				ans=ans[:l+1]+p+ans[l+1:]
				break
	print (ans)
else:
	o=x//2
	c0=a
	c1=b
	if (a>=b):
		ans=m
	else:
		ans=n

	z=len(ans)-1	
	for k in range(o):
		c=0
		while (c<z):
			if (a>=b):
				if (ans[c]==ans[c+1]):
					ans=ans[:c+1]+'1'+ans[c+1:]
					c1-=1
					z+=1

					break
				c+=1
			else:
				if (ans[c]==ans[c+1]):
					ans=ans[:c+1]+'0'+ans[c+1:]
					c0-=1
					z+=1
		
					break
				c+=1
	
	if (ans[len(ans)-1]=='0'):
		for i in range(c1):
			ans+='1'
	else:
		for i in range(c0):
			ans+='0'
	print (ans)







