Constructing Tests

1000ms

262144K

Description:

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 x₁, x₂, ..., x_t. For every $\text{[math]}$ , 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.

Input:

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.

Output:

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.

Sample Input:

Sample Output:

5 2
1 1
-1

Informação

Provedor Codeforces

Código CF938C