A12458 | Meaningless Operations

Can the greatest common divisor and bitwise operations have anything in common? It is time to answer this question.

Suppose you are given a positive integer $a$ . You want to choose some integer $b$ from $1$ to $a - 1$ inclusive in such a way that the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of integers $a \oplus b$ and $a \> \& \> b$ is as large as possible. In other words, you'd like to compute the following function:

$$$$f(a) = \max_{0 < b < a}{gcd(a \oplus b, a \> \& \> b)}. $$ </p><p>Here $\\oplus$ denotes the <a href="https://en.wikipedia.org/wiki/Bitwise_operation#XOR">bitwise XOR operation</a>, and $\\&$ denotes the <a href="https://en.wikipedia.org/wiki/Bitwise_operation#AND">bitwise AND operation</a>.</p><p>The greatest common divisor of two integers $x$ and $y$ is the largest integer $g$ such that both $x$ and $y$ are divided by $g$ without remainder.</p><p>You are given $q$ integers $a\_1, a\_2, \\ldots, a\_q$ . For each of these integers compute the largest possible value of the greatest common divisor (when $b$$$ is chosen optimally).

The first line contains an integer $q$ ( $1 \le q \le 10^3$ ) — the number of integers you need to compute the answer for.

After that $q$ integers are given, one per line: $a_1, a_2, \ldots, a_q$ ( $2 \le a_i \le 2^{25} - 1$ ) — the integers you need to compute the answer for.

For each integer, print the answer in the same order as the integers are given in input.