Binary String Constructing

1000ms

262144K

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.

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.

Sample Input:

2 2 1

Sample Output:

Sample Input:

3 3 3

Sample Output:

Sample Input:

5 3 6

Sample 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.

Informação

Provedor Codeforces

Código CF1003B