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. 
arr = list(map(int, input().split()))
a = arr[0]
b = arr[1]
x = arr[2]

arr = [False for i in range(a+b)]
arr = []

if(a>=b):
	arr.append(False)
	arr.append(True)
else:
	arr.append(True)
	arr.append(False)
a2 = a
b2 = b
a -= 1
b -= 1
x -=1
pos = 1
if(x>0):
	for i in range(2,a2+b2):
		if(x>0):
			arr.append(not arr[i-1])
			if(arr[i] == False) :
				a -= 1
			else:
				b -=1
			x -= 1
		else:
			pos = i
			break
leng = len(arr)
while(leng != (a2+b2)):
	if(a>0):
		if(arr[0]==False):
			for i in range(a):
				# print(arr)
				arr = [False] + arr
				# print(arr)
		else:
			arr2 = []
			for i in range(a):
				arr2.append(False)
			truepos = arr.index(False)
			arr = arr[0:truepos] + arr2 + arr[truepos:]
		leng += a
	if(b>0):
		if(arr[0]==True):
			for i in range(b):
				arr = [True] + arr
		else:
			arr2 = []
			for i in range(b):
				arr2.append(True)
			truepos = arr.index(True)
			arr = arr[0:truepos] + arr2 + arr[truepos:]
		leng += b



for i in range(len(arr)):
	if(arr[i]==False):
		print(0, end="")
	else:
		print(1, end="")
print()