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=input().split();
a=int(a);
b=int(b);
x=int(x);

y=x;
aa=a;
bb=b;
s="";
one="1";
zero="0";

if(b>a):
	s=s+one;
	b-=1;
	count=0;
            
	while(x>0):
		if(count%2==0):
			s=s+zero;
			a-=1;
		else:
			s=s+one;
			b-=1;
                
		count+=1;
		x-=1;
         
else:
	s=s+zero;
	a-=1;
	count=0;
	while(x>0):
		if(count%2==1):
			s=s+zero;
			a-=1;
		else:
			s=s+one;
			b-=1;
                
		count+=1;
		x-=1;
         
ans_one="";
ans_zero="";

for i in range(a):
	ans_zero+=zero;
        
for i in range(b):
	ans_one+=one;
        
if (aa>=bb):
	s=ans_zero+s;
	if(y%2==0):
		s=s[0:len(s)-1];
		s=s+ans_one;
		s=s+zero;
            
	else:
		s=s+ans_one;
         
else:
	s=ans_one+s;
	if(y%2==0):
		s=s[0:len(s)-1];
		s=s+ans_zero;
		s=s+one;
            
	else:
		s=s+ans_zero;

print(s);