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. 
def sexy(a,b,x,zero):
	ones=[]
	for i in range(a):
		ones.append(1)
		ones.append(3)
	ones.pop()
	three=ones.count(3)
	c=x
	while(c>1):
		if(c-2>=0):
			if(three>0):
				indi=ones.index(3)
				ones[indi]=0
				zero=zero-1
				three=three-1
				c=c-2
			else:
				break
		else:
			break
	done=c
	for i in range(len(ones)):
		if(ones[i]==1):
			print(ones[i],end='')
		elif(ones[i]==0 and done==0):
			for i in range(zero+1):
				print('0',end='')
				done=1
		elif(ones[i]==0):
			print('0',end='')


	if(c!=0):
		for i in range(zero):
			print('0',end='')
def sexy1(a,b,x,zero):
	ones=[]
	for i in range(a):
		ones.append(0)
		ones.append(3)
	ones.pop()
	three=ones.count(3)
	c=x
	while(c>1):
		if(c-2>=0):
			if(three>0):
				indi=ones.index(3)
				ones[indi]=1
				zero=zero-1
				three=three-1
				c=c-2
			else:
				break
		else:
			break
	done=c
	for i in range(len(ones)):
		if(ones[i]==0):
			print(ones[i],end='')
		elif(ones[i]==1 and done==0):
			for i in range(zero+1):
				print('1',end='')
				done=1
		elif(ones[i]==1):
			print('1',end='')
	if(c!=0):
		for i in range(zero):
			print('1',end='')
l=input().split()
a=int(l[0])
b=int(l[1])
x=int(l[2])
temp=a
a=b
b=temp
if(a>=b):
	sexy(a,b,x,b)
else:
	sexy1(b,a,x,a)