CF938C.Constructing Tests

Let's denote a m-free matrix as a binary (that is, consisting of only 1's and 0's) matrix such that every square submatrix of size m × m of this matrix contains at least one zero.

Consider the following problem:

You are given two integers n and m. You have to construct an m-free square matrix of size n × n such that the number of 1's in this matrix is maximum possible. Print the maximum possible number of 1's in such matrix.

You don't have to solve this problem. Instead, you have to construct a few tests for it.

You will be given t numbers _x_1, _x_2, ..., x__t. For every , find two integers n__i and m__i (n__i ≥ m__i) such that the answer for the aforementioned problem is exactly x__i if we set n = n__i and m = m__i.

我们称一个 m-自由矩阵为一个二进制矩阵（即仅由 1 和 0 构成），满足该矩阵的每个大小为 m × m 的方子矩阵中至少包含一个 0。

考虑如下问题：

给定两个整数 n 和 m，你需要构造一个大小为 n × n 的 m-自由方阵，使得该矩阵中 1 的个数尽可能多。输出该矩阵中 1 的最大可能个数。

你无需求解该问题，而只需为其构造若干测试用例。

你将获得 t 个数字 _x_₁, _x_₂, ..., x__t。对每个 ，请找出两个整数 n__i 和 m__i（满足 n__i ≥ m__i），使得当 n = n__i 且 m = m__i 时，上述问题的答案恰好为 x__i。

The first line contains one integer t (1 ≤ t ≤ 100) — the number of tests you have to construct.

Then t lines follow, i-th line containing one integer x__i (0 ≤ x__i ≤ 109).

Note that in hacks you have to set t = 1.

第一行包含一个整数 $t$（$1 \leq t \leq 100$）—— 你需要构造的测试用例数量。

接下来是 $t$ 行，其中第 $i$ 行包含一个整数 $x_i$（$0 \leq x_i \leq 10^9$）。

注意：在 hack 中，你必须设置 $t = 1$。

For each test you have to construct, output two positive numbers n__i and m__i (1 ≤ m__i ≤ n__i ≤ 109) such that the maximum number of 1's in a m__i-free n__i × n__i matrix is exactly x__i. If there are multiple solutions, you may output any of them; and if this is impossible to construct a test, output a single integer  - 1.

对于每个测试用例，你需要构造两个正整数 $n_i$ 和 $m_i$（满足 $1 \leq m_i \leq n_i \leq 10^9$），使得一个 $m_i$-free 的 $n_i \times n_i$ 矩阵中 1 的最大个数恰好为 $x_i$。若存在多个解，输出任意一个即可；若无法构造出满足条件的测试用例，则输出单个整数 $-1$。