Weird Function

You are given a positive integer $a$. Choose an integer $b$ with $1 \le b \le a - 1$ so that the greatest common divisor of $a \oplus b$ and $a \otimes b$ is as large as possible, and print that value. In other words, find $f(A)$ where $f(a) = \max_{0<b<a} \gcd(a \oplus b, a \otimes b)$ Here $\oplus$ is bitwise XOR and $\otimes$ is bitwise AND. The operations on single bits are defined by the table below.

For longer numbers, the operation is applied to the binary digits of the two operands position by position, and the resulting bits form the answer in binary. For example, $101 \oplus 11 = 110$ and $101 \otimes 11 = 1$, while $111 \oplus 101010 = 101101$ and $111 \otimes 101010 = 10$.

The first line contains the number of queries $N$ ($1 \le N \le 1\,000$). Each of the next $N$ lines contains one integer $A_i$ ($2 \le A_i < 2^{25}$).

Print $N$ lines. On line $i$, print the value of $f(A_i)$.