A14607. Consecutive Sum Riddle

Theofanis has a riddle for you and if you manage to solve it, he will give you a Cypriot snack halloumi for free (Cypriot cheese).

You are given an integer $n$ . You need to find two integers $l$ and $r$ such that $-10^{18} \le l < r \le 10^{18}$ and $l + (l + 1) + \ldots + (r - 1) + r = n$ .

The first line contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases.

The first and only line of each test case contains a single integer $n$ ( $1 \le n \le 10^{18}$ ).

For each test case, print the two integers $l$ and $r$ such that $-10^{18} \le l < r \le 10^{18}$ and $l + (l + 1) + \ldots + (r - 1) + r = n$ .

It can be proven that an answer always exists. If there are multiple answers, print any.

In the first test case, $0 + 1 = 1$ .

In the second test case, $(-1) + 0 + 1 + 2 = 2$ .

In the fourth test case, $1 + 2 + 3 = 6$ .

In the fifth test case, $18 + 19 + 20 + 21 + 22 = 100$ .

In the sixth test case, $(-2) + (-1) + 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 = 25$ .