A14894. K-good

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.

$6$ is a $3$ -good number since it can be expressed as a sum of $3$ numbers which give different remainders when divided by $3$ : $6 = 1 + 2 + 3$ .

$15$ is also a $3$ -good number since $15 = 1 + 5 + 9$ and $1, 5, 9$ give different remainders when divided by $3$ .

$20$ is a $5$ -good number since $20 = 2 + 3 + 4 + 5 + 6$ and $2,3,4,5,6$ give different remainders when divided by $5$ .