CF1343A.Candies

Recently Vova found $n$ candy wrappers. He remembers that he bought $x$ candies during the first day, $2x$ candies during the second day, $4x$ candies during the third day, $\dots$ , $2^{k-1} x$ candies during the $k$ -th day. But there is an issue: Vova remembers neither $x$ nor $k$ but he is sure that $x$ and $k$ are positive integers and $k > 1$ .

Vova will be satisfied if you tell him any positive integer $x$ so there is an integer $k>1$ that $x + 2x + 4x + \dots + 2^{k-1} x = n$ . It is guaranteed that at least one solution exists. Note that $k > 1$ .

You have to answer $t$ independent test cases.

The first line of the input contains one integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases. Then $t$ test cases follow.

The only line of the test case contains one integer $n$ ( $3 \le n \le 10^9$ ) — the number of candy wrappers Vova found. It is guaranteed that there is some positive integer $x$ and integer $k>1$ that $x + 2x + 4x + \dots + 2^{k-1} x = n$ .

Print one integer — any positive integer value of $x$ so there is an integer $k>1$ that $x+2x+4x+⋯+2^{k-1}x=n$.

In the first test case of the example, one of the possible answers is $x=1, k=2$ . Then $1 \cdot 1 + 2 \cdot 1$ equals $n=3$ .

In the second test case of the example, one of the possible answers is $x=2, k=2$ . Then $1 \cdot 2 + 2 \cdot 2$ equals $n=6$ .

In the third test case of the example, one of the possible answers is $x=1, k=3$ . Then $1 \cdot 1 + 2 \cdot 1 + 4 \cdot 1$ equals $n=7$ .

In the fourth test case of the example, one of the possible answers is $x=7, k=2$ . Then $1 \cdot 7 + 2 \cdot 7$ equals $n=21$ .

In the fifth test case of the example, one of the possible answers is $x=4, k=3$ . Then $1 \cdot 4 + 2 \cdot 4 + 4 \cdot 4$ equals $n=28$ .