A14894 | $K-good$

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题目描述

We say that a positive integer $n$ is $k$ -good for some positive integer $k$ if $n$ can be expressed as a sum of $k$ positive integers which give $k$ distinct remainders when divided by $k$ . Given a positive integer $n$ , find some $k \geq 2$ so that $n$ is $k$ -good or tell that such a $k$ does not exist.

The input consists of multiple test cases. The first line contains a single integer $t$ ( $1 \leq t \leq 10^5$ ) — the number of test cases. Each test case consists of one line with an integer $n$ ( $2 \leq n \leq 10^{18}$ ).

For each test case, print a line with a value of $k$ such that $n$ is $k$ -good ( $k \geq 2$ ), or $-1$ if $n$ is not $k$ -good for any $k$ . If there are multiple valid values of $k$ , you can print any of them.

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C++ 编辑器

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