#P1003B. Binary String Constructing

    ID: 6374 Type: RemoteJudge 1000ms 256MiB Tried: 0 Accepted: 0 Difficulty: (None) Uploaded By: Tags>constructive algorithms*1300

Binary String Constructing

No submission language available for this problem.

Description

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 $1 \le i < n$) 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.

The first line of the input contains three integers $a$, $b$ and $x$ ($1 \le a, b \le 100, 1 \le x < a + b)$.

Print only one string $s$, where $s$ is any binary string satisfying conditions described above. It is guaranteed that the answer always exists.

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.

Samples

2 2 1

1100

3 3 3

101100

5 3 6

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.