Let the closure of a positive integer (x \gt 0) be the following infinite binary string (C(x)): Write (x) in binary form without leading zeros; Concatenate the obtained string with itself infinitely many times and call the result (C(x)). For example, (C(1)) (=) 11111... , (C(4)) (=) 10010010010010... , (C(9)) (=) 100110011001... . Let the product of two closures (C(x) \mathop{\&} C(y)) be the infinite binary string obtained by the bitwise binary AND of the strings (C(x)) and (C(y)). For example, for (C(4) \mathop{\&} C(9)) we get () \begin{array}{r} \begin{array}{r} C(4)\\ C(9)\\ \end{array} \mathop{\&} \begin{array}{r} 100100100100100100...\\ 100110011001100110...\\ \end{array} \\ \hline \begin{array}{r} 100100000000100100... \end{array} \end{array} () You are given three integers (l), (r), and (n). Among all numbers in the segment (l, r), find two integers (x) and (y) ((l \le x \lt y \le r)) such that (C(x) \mathop{\&} C(y)) is lexicographically smallest , and print the first (n) binary symbols of this product. The first line contains one integer (t) ((1 \le t \le 1000)) — the number of test cases. The only line of each test case contains three integers (l), (r), and (n) ((1 \le l \lt r \lt 2^{30}); (1 \le n \le 1000)) — the range of possible values and the length of the answer. For each test case, print one binary string of length (n) — the first (n) symbols of the lexicographically smallest product of closures. In the first test case, the lexicographically smallest string is obtained by the product (C(2) \mathop{\&} C(4)).