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]=[int(i) for i in input().split()]

mini=min(a,b)

s=""
a_str=""
b_str=""

if(x%2==0):

	#if(a==b==x):

	#	for g in range(x//2):
	#		s+="0110"

	#	print(s)

	if(mini==a):

		for r in range(x//2):
			s+="10"
			a-=1
			b-=1

		s+="1"
		b-=1

		for d in range(b):
			b_str+="1"

		for e in range(a):
			a_str+="0"

		for w in range(len(s)):
			if(s[w]=="0"):
				s=s[0:w+1]+a_str+s[w+1:]
				break

		print(s+b_str)

	else:

		for r in range(x//2):
			s+="01"
			a-=1
			b-=1
		s+="0"
		a-=1

		for d in range(a):
			a_str+="0"

		for e in range(b):
			b_str+="1"

		for w in range(len(s)):
			if(s[w]=="1"):
				s=s[0:w+1]+b_str+s[w+1:]
				break

		print(s+a_str)	

else:

	if(mini==a):

		for r in range((x+1)//2):
			s+="10"
			a-=1
			b-=1

		for d in range(b):
			b_str+="1"

		for e in range(a):
			a_str+="0"


		print(b_str+s+a_str)


	else:

		for r in range((x+1)//2):
			s+="01"
			a-=1
			b-=1

		for d in range(a):
			a_str+="0"

		for e in range(b):
			b_str+="1"


		print(a_str+s+b_str)	


# for r in range(1,x+1):
# 	#if(r%2==0):
# 	s+="10"
# 	b-=1
# 	#else:
# 	#s+="01"
# 	a-=1

# for e in range(a):
# 	a_str+="0"


# for f in range(b):
# 	b_str+="1"

# print(b_str+s+a_str)

# elif(mini==b):

# 	for d in range(1,x+1):
# 		if(d%2==0):
# 			s+="01"
# 			a-=1
# 		else:
# 			s+="10"
# 			b-=1

# 	for e in range(a):
# 		a_str+="0"

# 	for f in range(b):
# 		b_str+="1"

# 	print()
