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 solve(zeros, ones, changes):
	if max(zeros, ones) > min(zeros, ones):
		max_changes = min(zeros, ones) * 2
	else:
		max_changes = min(zeros, ones) * 2 - 1
	assert changes <= max_changes

	if changes % 2 == 1:
		multiple = (changes + 1) // 2
		ans = "01" * multiple
		zeros_have = multiple
		ones_have = multiple
		return "0" * (zeros - zeros_have) + ans + "1" * (ones - ones_have)
	else:
		multiple = changes // 2
		if zeros > ones:
			return "01" * multiple + "1" * (ones - multiple) + "0" * (zeros - multiple)
		else:
			return "10" * multiple + "0" * (zeros - multiple) + "1" * (ones - multiple)


def check(zeros, ones, changes):
	ans = solve(zeros, ones, changes)
	print("solve({}, {}, {}) => {}".format(zeros, ones, changes, ans))
	assert len(ans) == zeros + ones
	assert sum([1 for digit in ans if digit == "1"]) == ones
	assert sum([1 for digit in ans if digit == "0"]) == zeros
	previous = None
	ans_changes = 0
	for digit in ans:
		if previous is not None:
			if digit != previous:
				ans_changes += 1
		previous = digit
		
	assert ans_changes == changes

zeros, ones, changes = map(int, input().split())
print(solve(zeros, ones, changes))
# check(2, 2, 3)
# check(4, 2, 3)
# check(5, 5, 3)
# check(2, 1, 2)
# check(2, 2, 2)
# check(5, 3, 6)
# check(4, 4, 4)
# check(5, 0, 0)
# check(0, 5, 0)
# check(1, 5, 1)
# check(3, 3, 3)
# check(2, 5, 1)
# check(2, 5, 1)
# check(10, 10, 1)
# check(4, 4, 4)
# check(4, 3, 3)
# check(3, 2, 4)