F. Binary String Reconstructiontime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputFor 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.InputThe 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.OutputPrint 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.ExampleInput
7
1 3 5
1 1 1
3 9 3
0 1 0
3 1 2
0 0 3
2 0 0
Output
1110011110
0011
0110001100101011
10
0000111
1111
000

7
1 3 5
1 1 1
3 9 3
0 1 0
3 1 2
0 0 3
2 0 0

1110011110 0011 0110001100101011 10 0000111 1111 000 
['constructive algorithms', 'dfs and similar', 'math', '*1500']