Binary String Reconstruction

1000ms

262144K

Description:

For some binary string $$$s$$$ (i.e. each character $$$s_i$$$ is either '0' or '1'), all pairs of consecutive (adjacent) characters were written. In other words, all substrings of length $$$2$$$ were written. For each pair (substring of length $$$2$$$), the number of '1' (ones) in it was calculated.

You are given three numbers:

$$$n_0$$$ — the number of such pairs of consecutive characters (substrings) where the number of ones equals $$$0$$$;
$$$n_1$$$ — the number of such pairs of consecutive characters (substrings) where the number of ones equals $$$1$$$;
$$$n_2$$$ — the number of such pairs of consecutive characters (substrings) where the number of ones equals $$$2$$$.

For example, for the string $$$s=$$$"1110011110", the following substrings would be written: "11", "11", "10", "00", "01", "11", "11", "11", "10". Thus, $$$n_0=1$$$, $$$n_1=3$$$, $$$n_2=5$$$.

Your task is to restore any suitable binary string $$$s$$$ from the given values $$$n_0, n_1, n_2$$$. It is guaranteed that at least one of the numbers $$$n_0, n_1, n_2$$$ is greater than $$$0$$$. Also, it is guaranteed that a solution exists.

Input:

The first line contains an integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases in the input. Then test cases follow.

Each test case consists of one line which contains three integers $$$n_0, n_1, n_2$$$ ($$$0 \le n_0, n_1, n_2 \le 100$$$; $$$n_0 + n_1 + n_2 > 0$$$). It is guaranteed that the answer for given $$$n_0, n_1, n_2$$$ exists.

Output:

Print $$$t$$$ lines. Each of the lines should contain a binary string corresponding to a test case. If there are several possible solutions, print any of them.

Sample Input:

Sample Output:

1110011110
0011
0110001100101011
10
0000111
1111
000

Informação

Provedor Codeforces

Código CF1352F