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. 
(Niswanob1,fuscat1,Chri1)=[int(Chri1) for 
Chri1 in       raw_input().split()]
Chri2=[1,0]
Niswanob1-=1
Niswanob2=0
fuscat1-=1
weffw = Niswanob1
if weffw == 2:
	Chri1-=1
else:
	Chri1-=1
if ((Chri1%2)==0):
 fuscat2=(Chri1//2)
 Chri2=(Chri2 + ([1,0]*    fuscat2))
 Niswanob1-=fuscat2
 fuscat1-=fuscat2
 Chri2=((([1]*    fuscat1) + Chri2) + ([0]*    Niswanob1))
else:
 fuscat2=(Chri1//2)
 Chri2=(Chri2 + ([1,0]*    fuscat2))
 Niswanob1-=fuscat2
 fuscat1-=fuscat2
 if (fuscat1>0):
  Chri2=((Chri2 + ([0]*    Niswanob1)) + ([1]*    fuscat1))
 else:
  Chri2=((([0]*    Niswanob1) + ([1]*    fuscat1)) + Chri2)


print ''.join([str(Chri2[bitboostdotcom1]) for bitboostdotcom1 in       range(0,len(Chri2))])

