Codeforces Round 636 (Div. 3) |
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Finished |

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brute force

math

*900

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A. Candies

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputRecently 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.

Input

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 $$$x + 2x + 4x + \dots + 2^{k-1} x = n$$$.

Output

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

Example

Input

7 3 6 7 21 28 999999999 999999984

Output

1 2 1 7 4 333333333 333333328

Note

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 $$$n=28$$$.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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