A13413 | $Candies$

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题目描述

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 $x+2x+4x+⋯+2^{k-1}x=n$.

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C++ 编辑器

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