AND Until Zero

An old machine has a single register. You load the number $n$ into it, and then the machine starts counting down: it ANDs the register with $n-1$, then with $n-2$, then with $n-3$, and so on, one number at a time.

Sooner or later the register turns into $0$, and once it does it can never come back. Your task is to report the number the machine was at in that moment.

Formally, find the largest $k$ for which

where $\&$ denotes the bitwise AND operation. The value $k=0$ is allowed - the machine is happy to count all the way down.

Input

First line of input will be a single integer $t$ - the number of testcases.
Each of the next $t$ lines contains a single integer $n$ - the number loaded into the register.

Output

For every testcase print a single line with the largest such $k$.

Example

4
2
5
17
1

1
3
15
0

For $n=5$ the machine first does $5\&4=4$, which is not $0$ yet, and then $4\&3=0$ - so it stopped at $3$. For $n=1$ the register holds $1$ the whole time and only $1\&0$ empties it, so the answer is $0$.

Constraints

$1\le t\le 1000$
$1\le n\le 10^9$

This problem was adapted from And Then There Were K, problem A of Codeforces Round 721 (Div. 2).