CF1110C.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) of integers $a \oplus b$ and $a \ \gt \& \ \gt b$ is as large as possible. In other words, you'd like to compute the following function:

f(a) = \\max\_{0 \\lt b \\lt a}{gcd(a \\oplus b, a \\ \\gt \\& \\ \\gt b)}.

Here $\oplus$ denotes the bitwise XOR operation, and $\&$ denotes the bitwise AND operation.

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.

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).

最大公约数与位运算之间是否存在某种联系？现在是回答这个问题的时候了。

假设你给定一个正整数 $a$。你需要从 $1$ 到 $a - 1$（含端点）中选择某个整数 $b$，使得整数 $a \oplus b$ 与 $a \ \& \ b$ 的最大公约数（GCD） 尽可能大。换言之，你需要计算如下函数：

$$f(a) = \max_{0 < b < a}{\gcd(a \oplus b,\, a \ \& \ b)}.$$

其中 $\oplus$ 表示按位异或（XOR）运算，$\&$ 表示按位与（AND）运算。

两个整数 $x$ 和 $y$ 的最大公约数是指能同时整除 $x$ 和 $y$ 的最大整数 $g$。

你将获得 $q$ 个整数 $a_1, a_2, \ldots, a_q$。对其中每一个整数，请计算在最优选择 $b$ 的前提下所能达到的最大公约数值。

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.

第一行包含一个整数 $q$（$1 \le q \le 10^3$）—— 表示你需要计算答案的整数个数。

接下来给出 $q$ 个整数，每行一个：$a_1, a_2, \ldots, a_q$（$2 \le a_i \le 2^{25} - 1$）—— 表示你需要计算答案的整数。

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

对每个整数，按照输入中给出的顺序输出答案。

For the first integer the optimal choice is $b = 1$, then $a \oplus b = 3$, $a \ \gt \& \ \gt b = 0$, and the greatest common divisor of $3$ and $0$ is $3$.

For the second integer one optimal choice is $b = 2$, then $a \oplus b = 1$, $a \ \gt \& \ \gt b = 2$, and the greatest common divisor of $1$ and $2$ is $1$.

For the third integer the optimal choice is $b = 2$, then $a \oplus b = 7$, $a \ \gt \& \ \gt b = 0$, and the greatest common divisor of $7$ and $0$ is $7$.

对于第一个整数，最优选择是 $b = 1$，此时 $a \oplus b = 3$，$a \ \gt \& \ \gt b = 0$，而 $3$ 与 $0$ 的最大公约数为 $3$。

对于第二个整数，一个最优选择是 $b = 2$，此时 $a \oplus b = 1$，$a \ \gt \& \ \gt b = 2$，而 $1$ 与 $2$ 的最大公约数为 $1$。

对于第三个整数，最优选择是 $b = 2$，此时 $a \oplus b = 7$，$a \ \gt \& \ \gt b = 0$，而 $7$ 与 $0$ 的最大公约数为 $7$。