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B. Binary String Constructing

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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 $$$1 \le i < n$$$) such that $$$s_i \ne s_{i + 1}$$$. It is guaranteed that the answer always exists.

For example, for the string "01010" there are four indices $$$i$$$ such that $$$1 \le i < n$$$ and $$$s_i \ne s_{i + 1}$$$ ($$$i = 1, 2, 3, 4$$$). 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 $$$x$$$ ($$$1 \le a, b \le 100, 1 \le x < a + b)$$$.

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.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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