Codeforces Global Round 1 |
---|

Finished |

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

constructive algorithms

math

number theory

*1500

No tag edit access

The problem statement has recently been changed. View the changes.

×
C. Meaningless Operations

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputCan 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 $$$a \> \& \> b$$$ is as large as possible. In other words, you'd like to compute the following function:

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

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).

Input

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.

Output

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

Example

Input

3 2 3 5

Output

3 1 7

Note

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

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

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

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/16/2024 11:51:27 (h2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|